In many industrial robotic applications there is a need to track periodic reference signals and/or reject periodic disturbances. This paper presents a novel repetitive control design for systems with constant time-delays in both forward and feedback control channels. An additional delay is introduced together with plant delays to construct an internal model for periodic signals, and a simple proportional control is utilized to stabilize the closed-loop system. Sufficient stability conditions of the closed-loop system and the robustness analysis under modeling uncertainties are studied. Experimental results are included to evaluate the validity and effectiveness of the proposed method.