diff --git a/src/schedule/message_passing.cc b/src/schedule/message_passing.cc
index a144e7fc40d1..3cea560318d8 100644
--- a/src/schedule/message_passing.cc
+++ b/src/schedule/message_passing.cc
@@ -477,9 +477,14 @@ std::vector<Expr> MakeBoundCheck(
     CHECK(iv->dom.defined());
     if (!skip_ivar_domain && !iv->dom.same_as(dom)) {
       Expr value = ComputeExpr<Sub>(value_map.at(iv), iv->dom->min);
-      Expr vmax = EvalSet(value, iset_dmap).max();
+      IntSet s = EvalSet(value, iset_dmap);
+      Expr vmin = s.min();
+      Expr vmax = s.max();
+      if (vmin.type() != value.type() || !can_prove(vmin >= iv->dom->min)) {
+        preds.emplace_back(value >= 0);
+      }
       if (vmax.type() != value.type() || !can_prove(vmax < iv->dom->extent)) {
-        preds.emplace_back(value < iv->dom->extent);
+        preds.emplace_back(value < (iv->dom->extent - iv->dom->min));
       }
     }
   }
diff --git a/tests/python/unittest/test_pass_inject_copy_intrin.py b/tests/python/unittest/test_pass_inject_copy_intrin.py
index c6ed19d65b69..a44f3899c282 100644
--- a/tests/python/unittest/test_pass_inject_copy_intrin.py
+++ b/tests/python/unittest/test_pass_inject_copy_intrin.py
@@ -82,6 +82,7 @@ def test_copy_pad_split():
     Ab = tvm.decl_buffer(A.shape, A.dtype, name='A')
     Bb = tvm.decl_buffer(B.shape, B.dtype, name='B')
     stmt = tvm.ir_pass.StorageFlatten(stmt, {A: Ab, B: Bb}, 64)
+    stmt = tvm.ir_pass.Simplify(stmt)
     stmt = tvm.ir_pass.CanonicalSimplify(stmt)
     def cb(src, dst, pad_before, pad_after, pad_value):
         assert(dst.elem_offset.value == 0)
diff --git a/tests/python/unittest/test_schedule_schedule_ops.py b/tests/python/unittest/test_schedule_schedule_ops.py
index 03b8dbf48c8c..dd57c35c39b6 100644
--- a/tests/python/unittest/test_schedule_schedule_ops.py
+++ b/tests/python/unittest/test_schedule_schedule_ops.py
@@ -249,6 +249,18 @@ def test_schedule_cache_relayout3():
     stmt = tvm.schedule.ScheduleOps(s, bounds)
 
 
+def test_schedule_bound_condition():
+   A = tvm.placeholder((64,), name='A', dtype="float32")
+   Apad = tvm.compute((66,), lambda i: tvm.select(tvm.all(i>0, i < 65), A[i-1], tvm.const(0.)), name='Apad')
+   Apad2 = tvm.compute((66,), lambda i: Apad[i]*2, name='Apad2')
+   s = tvm.create_schedule(Apad2.op)
+   AL1 = s.cache_read(A,"local",[Apad])
+   s = s.normalize()
+   bounds = tvm.schedule.InferBound(s)
+   stmt = tvm.schedule.ScheduleOps(s, bounds)
+   stmt = tvm.ir_pass.Simplify(stmt)
+   assert (isinstance(stmt.body.body.first.body.body.then_case, tvm.stmt.IfThenElse))
+
 if __name__ == "__main__":
     test_schedule_middle_cache()
     test_inline_multi_reduce()
@@ -265,3 +277,4 @@ def test_schedule_cache_relayout3():
     test_schedule1()
     test_schedule2()
     test_schedule_cache()
+    test_schedule_bound_condition()