diff --git a/clippy_lints/src/missing_const_for_fn.rs b/clippy_lints/src/missing_const_for_fn.rs
index 89398f82c9e..2f20aa9c683 100644
--- a/clippy_lints/src/missing_const_for_fn.rs
+++ b/clippy_lints/src/missing_const_for_fn.rs
@@ -1,10 +1,11 @@
-use crate::utils::{is_entrypoint_fn, span_lint, trait_ref_of_method};
+use crate::utils::{has_drop, is_entrypoint_fn, span_lint, trait_ref_of_method};
 use rustc::hir;
 use rustc::hir::intravisit::FnKind;
-use rustc::hir::{Body, Constness, FnDecl, HirId};
+use rustc::hir::{Body, Constness, FnDecl, HirId, HirVec};
 use rustc::lint::{in_external_macro, LateContext, LateLintPass, LintArray, LintPass};
 use rustc::{declare_lint_pass, declare_tool_lint};
 use rustc_mir::transform::qualify_min_const_fn::is_min_const_fn;
+use rustc_typeck::hir_ty_to_ty;
 use syntax_pos::Span;
 
 declare_clippy_lint! {
@@ -94,7 +95,10 @@ impl<'a, 'tcx> LateLintPass<'a, 'tcx> for MissingConstForFn {
                 }
             },
             FnKind::Method(_, sig, ..) => {
-                if trait_ref_of_method(cx, hir_id).is_some() || already_const(sig.header) {
+                if trait_ref_of_method(cx, hir_id).is_some()
+                    || already_const(sig.header)
+                    || method_accepts_dropable(cx, &sig.decl.inputs)
+                {
                     return;
                 }
             },
@@ -113,6 +117,16 @@ impl<'a, 'tcx> LateLintPass<'a, 'tcx> for MissingConstForFn {
     }
 }
 
+/// Returns true if any of the method parameters is a type that implements `Drop`. The method
+/// can't be made const then, because `drop` can't be const-evaluated.
+fn method_accepts_dropable(cx: &LateContext<'_, '_>, param_tys: &HirVec<hir::Ty>) -> bool {
+    // If any of the params are dropable, return true
+    param_tys.iter().any(|hir_ty| {
+        let ty_ty = hir_ty_to_ty(cx.tcx, hir_ty);
+        has_drop(cx, ty_ty)
+    })
+}
+
 // We don't have to lint on something that's already `const`
 fn already_const(header: hir::FnHeader) -> bool {
     header.constness == Constness::Const
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 115cc954dc7..f367279906f 100644
--- a/tests/ui/missing_const_for_fn/cant_be_const.rs
+++ b/tests/ui/missing_const_for_fn/cant_be_const.rs
@@ -68,3 +68,25 @@ impl std::ops::Add for Point {
         Point(self.0 + other.0, self.1 + other.1)
     }
 }
+
+mod with_drop {
+    pub struct A;
+    pub struct B;
+    impl Drop for A {
+        fn drop(&mut self) {}
+    }
+
+    impl A {
+        // This can not be const because the type implements `Drop`.
+        pub fn a(self) -> B {
+            B
+        }
+    }
+
+    impl B {
+        // This can not be const because `a` implements `Drop`.
+        pub fn a(self, a: A) -> B {
+            B
+        }
+    }
+}
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 139e64de1ff..9109d255ca7 100644
--- a/tests/ui/missing_const_for_fn/could_be_const.rs
+++ b/tests/ui/missing_const_for_fn/could_be_const.rs
@@ -53,5 +53,20 @@ fn generic_arr<T: Copy>(t: [T; 1]) -> T {
     t[0]
 }
 
+mod with_drop {
+    pub struct A;
+    pub struct B;
+    impl Drop for A {
+        fn drop(&mut self) {}
+    }
+
+    impl B {
+        // This can be const, because `a` is passed by reference
+        pub fn b(self, a: &A) -> B {
+            B
+        }
+    }
+}
+
 // Should not be const
 fn main() {}
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 22ea852905d..0c0775764b7 100644
--- a/tests/ui/missing_const_for_fn/could_be_const.stderr
+++ b/tests/ui/missing_const_for_fn/could_be_const.stderr
@@ -49,5 +49,13 @@ LL | |     t
 LL | | }
    | |_^
 
-error: aborting due to 6 previous errors
+error: this could be a const_fn
+  --> $DIR/could_be_const.rs:65:9
+   |
+LL | /         pub fn b(self, a: &A) -> B {
+LL | |             B
+LL | |         }
+   | |_________^
+
+error: aborting due to 7 previous errors