Typing text passwords is challenging when using touchscreens on mobile devices and this is becoming more problematic as mobile usage increases. We designed a new graphical password scheme called Touchscreen Multi-layered Drawing(TMD) specifically for use with touchscreens. We conducted an exploratory user study of three existing graphical passwords on smart phones and tablets with 31 users. From this, we set our design goals for TMD to include addressing input accuracy issues without having to memorize images, while maintaining an appropriately secure password space. Design features include warp cells which allow TMD users to continuously draw their passwords across multiple layers in order to create more complex passwords than normally possible on a small screen. We compared the usability of TMD to Draw A Secret (DAS) on a tablet computer and a smart phone with 90 users. Results show that TMD improves memorability, addresses the input accuracy issues, and is preferred as a replacement for text passwords on mobile devices.