A motion-based authentication method is operative in a mobile computing device having a display interface and that includes an accelerometer. Normally, the device software includes a locking mechanism that automatically locks the display interface after a configurable timeout. The authentication method operates to un-lock the display interface (and thus allow the user access to the device) by movement of the device in a predetermined series of physical movements and without display-based entry of a password or other access code on the display itself. In this manner, the user can un-lock the device without display-based entry of a password (on the display itself) by simply holding the device and performing the necessary movement(s) to generate the unique code.