diff --git a/src/librustdoc/clean/types.rs b/src/librustdoc/clean/types.rs
index 5c63efef717d1..87de41fde63c5 100644
--- a/src/librustdoc/clean/types.rs
+++ b/src/librustdoc/clean/types.rs
@@ -676,7 +676,8 @@ impl Item {
         }
         let header = match *self.kind {
             ItemKind::ForeignFunctionItem(_) => {
-                let abi = tcx.fn_sig(self.item_id.as_def_id().unwrap()).abi();
+                let def_id = self.item_id.as_def_id().unwrap();
+                let abi = tcx.fn_sig(def_id).abi();
                 hir::FnHeader {
                     unsafety: if abi == Abi::RustIntrinsic {
                         intrinsic_operation_unsafety(tcx, self.item_id.as_def_id().unwrap())
@@ -684,7 +685,14 @@ impl Item {
                         hir::Unsafety::Unsafe
                     },
                     abi,
-                    constness: hir::Constness::NotConst,
+                    constness: if abi == Abi::RustIntrinsic
+                        && tcx.is_const_fn(def_id)
+                        && is_unstable_const_fn(tcx, def_id).is_none()
+                    {
+                        hir::Constness::Const
+                    } else {
+                        hir::Constness::NotConst
+                    },
                     asyncness: hir::IsAsync::NotAsync,
                 }
             }
diff --git a/tests/rustdoc/const-intrinsic.rs b/tests/rustdoc/const-intrinsic.rs
new file mode 100644
index 0000000000000..2fc486d01dae0
--- /dev/null
+++ b/tests/rustdoc/const-intrinsic.rs
@@ -0,0 +1,25 @@
+#![feature(intrinsics)]
+#![feature(staged_api)]
+
+#![crate_name = "foo"]
+#![stable(since="1.0.0", feature="rust1")]
+
+extern "rust-intrinsic" {
+    // @has 'foo/fn.transmute.html'
+    // @has - '//pre[@class="rust fn"]' 'pub const unsafe extern "rust-intrinsic" fn transmute<T, U>(_: T) -> U'
+    #[stable(since="1.0.0", feature="rust1")]
+    #[rustc_const_stable(feature = "const_transmute", since = "1.56.0")]
+    pub fn transmute<T, U>(_: T) -> U;
+
+    // @has 'foo/fn.unreachable.html'
+    // @has - '//pre[@class="rust fn"]' 'pub unsafe extern "rust-intrinsic" fn unreachable() -> !'
+    #[stable(since="1.0.0", feature="rust1")]
+    pub fn unreachable() -> !;
+}
+
+extern "C" {
+    // @has 'foo/fn.needs_drop.html'
+    // @has - '//pre[@class="rust fn"]' 'pub unsafe extern "C" fn needs_drop() -> !'
+    #[stable(since="1.0.0", feature="rust1")]
+    pub fn needs_drop() -> !;
+}