In this paper, a new method for color-image encryption using discrete quaternion fourier-transforms (DQFT) combined with doubled random-phase encryption as used in the optical implementation is proposed, by which color images can be processed as a whole, rather than as separated color components in three channels, so that the complexity of the encryption system can be effectively reduced without any reduction in its security. The principle of both encryption and decryption is detailed and the robustness of the system has been examined experimentally.