diff --git a/include/fmt/format.h b/include/fmt/format.h
index 6b03e857fa066..5d90f443fb008 100644
--- a/include/fmt/format.h
+++ b/include/fmt/format.h
@@ -742,9 +742,11 @@ void basic_memory_buffer<T, SIZE, Allocator>::grow(size_t size) {
 #ifdef FMT_FUZZ
   if (size > 5000) throw std::runtime_error("fuzz mode - won't grow that much");
 #endif
+  const size_t max_size = std::allocator_traits<Allocator>::max_size(alloc_);
   size_t old_capacity = this->capacity();
   size_t new_capacity = old_capacity + old_capacity / 2;
   if (size > new_capacity) new_capacity = size;
+  else if (new_capacity > max_size) new_capacity = (std::max)(size, max_size);
   T* old_data = this->data();
   T* new_data =
       std::allocator_traits<Allocator>::allocate(alloc_, new_capacity);
diff --git a/test/format-test.cc b/test/format-test.cc
index 128b57a2e10ee..bdc3c1c229cf3 100644
--- a/test/format-test.cc
+++ b/test/format-test.cc
@@ -354,6 +354,33 @@ TEST(MemoryBufferTest, ExceptionInDeallocate) {
   EXPECT_CALL(alloc, deallocate(&mem2[0], 2 * size));
 }
 
+TEST(MemoryBufferTest, AllocatorMaxSize) {
+  // 160 = 128 + 32
+  typedef allocator_max_size<std::allocator<char>, 160> TestAllocator;
+  basic_memory_buffer<char, 10, TestAllocator> buffer;
+  buffer.resize(128);
+  bool throws_on_resize = false;
+  try {
+    // new_capacity = 128 + 128/2 = 192 > 160
+    buffer.resize(160);
+  } catch (const std::exception &) {
+    throws_on_resize = true;
+  }
+  EXPECT_EQ(throws_on_resize, false);
+}
+
+TEST(MemoryBufferTest, AllocatorMaxSizeOverflow) {
+  typedef allocator_max_size<std::allocator<char>, 160> TestAllocator;
+  basic_memory_buffer<char, 10, TestAllocator> buffer;
+  bool throws_on_resize = false;
+  try {
+    buffer.resize(161);
+  } catch (const std::exception &) {
+    throws_on_resize = true;
+  }
+  EXPECT_EQ(throws_on_resize, true);
+}
+
 TEST(UtilTest, UTF8ToUTF16) {
   fmt::detail::utf8_to_utf16 u("лошадка");
   EXPECT_EQ(L"\x043B\x043E\x0448\x0430\x0434\x043A\x0430", u.str());
diff --git a/test/mock-allocator.h b/test/mock-allocator.h
index 513a62e8bb32c..af393db0121c6 100644
--- a/test/mock-allocator.h
+++ b/test/mock-allocator.h
@@ -57,4 +57,24 @@ template <typename Allocator> class allocator_ref {
   void deallocate(value_type* p, size_t n) { alloc_->deallocate(p, n); }
 };
 
+template <typename Allocator, size_t MaxSize>
+class allocator_max_size: public Allocator {
+ public:
+  typedef typename Allocator::value_type value_type;
+  size_t max_size() const FMT_NOEXCEPT {
+    return MaxSize;
+  }
+  value_type* allocate(size_t n) {
+    if (n > max_size()) {
+      throw std::length_error("size > max_size");
+    }
+    return std::allocator_traits<Allocator>::allocate(
+      *static_cast<Allocator *>(this), n);
+  }
+  void deallocate(value_type* p, size_t n) {
+    std::allocator_traits<Allocator>::deallocate(
+      *static_cast<Allocator *>(this), p, n);
+  }
+};
+
 #endif  // FMT_MOCK_ALLOCATOR_H_