diff --git a/src/librustdoc/clean/types.rs b/src/librustdoc/clean/types.rs
index 600c564d71418..2808339bb5560 100644
--- a/src/librustdoc/clean/types.rs
+++ b/src/librustdoc/clean/types.rs
@@ -647,7 +647,20 @@ impl Item {
         ) -> hir::FnHeader {
             let sig = tcx.fn_sig(def_id).skip_binder();
             let constness = if tcx.is_const_fn(def_id) {
-                hir::Constness::Const
+                // rustc's `is_const_fn` returns `true` for associated functions that have an `impl const` parent
+                // or that have a `#[const_trait]` parent. Do not display those as `const` in rustdoc because we
+                // won't be printing correct syntax plus the syntax is unstable.
+                match tcx.opt_associated_item(def_id) {
+                    Some(ty::AssocItem {
+                        container: ty::AssocItemContainer::Impl,
+                        trait_item_def_id: Some(_),
+                        ..
+                    })
+                    | Some(ty::AssocItem { container: ty::AssocItemContainer::Trait, .. }) => {
+                        hir::Constness::NotConst
+                    }
+                    None | Some(_) => hir::Constness::Const,
+                }
             } else {
                 hir::Constness::NotConst
             };
diff --git a/tests/rustdoc/constant/const-trait-and-impl-methods.rs b/tests/rustdoc/constant/const-trait-and-impl-methods.rs
new file mode 100644
index 0000000000000..30fc539e5533f
--- /dev/null
+++ b/tests/rustdoc/constant/const-trait-and-impl-methods.rs
@@ -0,0 +1,36 @@
+// check that we don't render `#[const_trait]` methods as `const` - even for
+// const `trait`s and `impl`s.
+#![crate_name = "foo"]
+#![feature(const_trait_impl)]
+
+//@ has foo/trait.Tr.html
+//@ has - '//*[@id="tymethod.required"]' 'fn required()'
+//@ !has - '//*[@id="tymethod.required"]' 'const'
+//@ has - '//*[@id="method.defaulted"]' 'fn defaulted()'
+//@ !has - '//*[@id="method.defaulted"]' 'const'
+#[const_trait]
+pub trait Tr {
+    fn required();
+    fn defaulted() {}
+}
+
+pub struct ConstImpl {}
+pub struct NonConstImpl {}
+
+//@ has foo/struct.ConstImpl.html
+//@ has - '//*[@id="method.required"]' 'fn required()'
+//@ !has - '//*[@id="method.required"]' 'const'
+//@ has - '//*[@id="method.defaulted"]' 'fn defaulted()'
+//@ !has - '//*[@id="method.defaulted"]' 'const'
+impl const Tr for ConstImpl {
+    fn required() {}
+}
+
+//@ has foo/struct.NonConstImpl.html
+//@ has - '//*[@id="method.required"]' 'fn required()'
+//@ !has - '//*[@id="method.required"]' 'const'
+//@ has - '//*[@id="method.defaulted"]' 'fn defaulted()'
+//@ !has - '//*[@id="method.defaulted"]' 'const'
+impl Tr for NonConstImpl {
+    fn required() {}
+}