diff --git a/clippy_lints/src/missing_const_for_fn.rs b/clippy_lints/src/missing_const_for_fn.rs
index 44ec1bd08cf..ed5f46ddc8d 100644
--- a/clippy_lints/src/missing_const_for_fn.rs
+++ b/clippy_lints/src/missing_const_for_fn.rs
@@ -8,6 +8,7 @@
 use rustc_hir::{self as hir, Body, Constness, FnDecl, GenericParamKind};
 use rustc_lint::{LateContext, LateLintPass};
 use rustc_middle::lint::in_external_macro;
+use rustc_middle::ty;
 use rustc_session::impl_lint_pass;
 use rustc_span::def_id::LocalDefId;
 use rustc_span::Span;
@@ -131,6 +132,10 @@ fn check_fn(
             FnKind::Closure => return,
         }
 
+        if fn_inputs_has_impl_trait_ty(cx, def_id) {
+            return;
+        }
+
         let hir_id = cx.tcx.local_def_id_to_hir_id(def_id);
 
         // Const fns are not allowed as methods in a trait.
@@ -185,3 +190,15 @@ fn could_be_const_with_abi(cx: &LateContext<'_>, msrv: &Msrv, abi: Abi) -> bool
         _ => cx.tcx.features().const_extern_fn,
     }
 }
+
+/// Return `true` when the given `def_id` is a function that has `impl Trait` ty as one of
+/// its parameter types.
+fn fn_inputs_has_impl_trait_ty(cx: &LateContext<'_>, def_id: LocalDefId) -> bool {
+    let inputs = cx.tcx.fn_sig(def_id).instantiate_identity().inputs().skip_binder();
+    inputs.iter().any(|input| {
+        matches!(
+            input.kind(),
+            ty::Alias(ty::AliasTyKind::Weak, alias_ty) if cx.tcx.type_of(alias_ty.def_id).skip_binder().is_impl_trait()
+        )
+    })
+}
diff --git a/tests/ui/missing_const_for_fn/cant_be_const.rs b/tests/ui/missing_const_for_fn/cant_be_const.rs
index 952ff828363..2c6e1e92da0 100644
--- a/tests/ui/missing_const_for_fn/cant_be_const.rs
+++ b/tests/ui/missing_const_for_fn/cant_be_const.rs
@@ -7,6 +7,7 @@
 
 #![warn(clippy::missing_const_for_fn)]
 #![feature(start)]
+#![feature(type_alias_impl_trait)]
 
 extern crate helper;
 extern crate proc_macros;
@@ -190,3 +191,11 @@ extern "C-unwind" fn c_unwind() {}
     extern "system" fn system() {}
     extern "system-unwind" fn system_unwind() {}
 }
+
+mod with_ty_alias {
+    type Foo = impl std::fmt::Debug;
+
+    fn foo(_: Foo) {
+        let _: Foo = 1;
+    }
+}
diff --git a/tests/ui/missing_const_for_fn/could_be_const.fixed b/tests/ui/missing_const_for_fn/could_be_const.fixed
index 572ca52439a..2311bd0acda 100644
--- a/tests/ui/missing_const_for_fn/could_be_const.fixed
+++ b/tests/ui/missing_const_for_fn/could_be_const.fixed
@@ -186,3 +186,18 @@ mod issue12677 {
         }
     }
 }
+
+mod with_ty_alias {
+    trait FooTrait {
+        type Foo: std::fmt::Debug;
+        fn bar(_: Self::Foo) {}
+    }
+    impl FooTrait for () {
+        type Foo = i32;
+    }
+    // NOTE: When checking the type of a function param, make sure it is not an alias with
+    // `AliasTyKind::Projection` before calling `TyCtxt::type_of` to find out what the actual type
+    // is. Because the associate ty could have no default, therefore would cause ICE, as demostrated
+    // in this test.
+    const fn alias_ty_is_projection(bar: <() as FooTrait>::Foo) {}
+}
diff --git a/tests/ui/missing_const_for_fn/could_be_const.rs b/tests/ui/missing_const_for_fn/could_be_const.rs
index 4d19c4d7a48..cb7733ed382 100644
--- a/tests/ui/missing_const_for_fn/could_be_const.rs
+++ b/tests/ui/missing_const_for_fn/could_be_const.rs
@@ -186,3 +186,18 @@ pub fn new(text: String) -> Self {
         }
     }
 }
+
+mod with_ty_alias {
+    trait FooTrait {
+        type Foo: std::fmt::Debug;
+        fn bar(_: Self::Foo) {}
+    }
+    impl FooTrait for () {
+        type Foo = i32;
+    }
+    // NOTE: When checking the type of a function param, make sure it is not an alias with
+    // `AliasTyKind::Projection` before calling `TyCtxt::type_of` to find out what the actual type
+    // is. Because the associate ty could have no default, therefore would cause ICE, as demostrated
+    // in this test.
+    fn alias_ty_is_projection(bar: <() as FooTrait>::Foo) {}
+}
diff --git a/tests/ui/missing_const_for_fn/could_be_const.stderr b/tests/ui/missing_const_for_fn/could_be_const.stderr
index ab36e0a281a..3cae5bcbc4a 100644
--- a/tests/ui/missing_const_for_fn/could_be_const.stderr
+++ b/tests/ui/missing_const_for_fn/could_be_const.stderr
@@ -261,5 +261,16 @@ help: make the function `const`
 LL |         pub const fn new(text: String) -> Self {
    |             +++++
 
-error: aborting due to 19 previous errors
+error: this could be a `const fn`
+  --> tests/ui/missing_const_for_fn/could_be_const.rs:202:5
+   |
+LL |     fn alias_ty_is_projection(bar: <() as FooTrait>::Foo) {}
+   |     ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+   |
+help: make the function `const`
+   |
+LL |     const fn alias_ty_is_projection(bar: <() as FooTrait>::Foo) {}
+   |     +++++
+
+error: aborting due to 20 previous errors