Considering that time-delay is frequently encountered in a variety of practical chaotic systems, we investigate the complete synchronization (CS) of coupled multiple-time-delay complex chaotic systems and design the control law by error feedback, which is simple in principle and easy to implement in engineering. A communication scheme is further designed according to chaotic masking. We take coupled multiple-time-delay complex Lorenz system as an example, make simulations and verify the effect of the controllers. The error feedback is extended to complex chaotic systems with multiple-time-delay. The CS of real chaotic systems and complex chaotic systems without time-delay are its special cases.