We propose a hybrid automatic repeat request (HARQ) scheme by using complementary punctured turbo (CPT) codes. The information bit sequence is encoded by a rate-1/3 convolutional turbo code, and then punctured by different sets of coded bits using complementary perforation patterns, which is used for turbo decoding. In our proposed HARQ process, the sets of coded bits are sent alternatively, and are combined with previous stored code sequence at the receiver. Using the same channel conditions, the conducted simulation results show that our proposed scheme is superior over the three well known HARQ schemes for a wide range of signal-to-noise ratios (SNRs) in terms of the average transmit power-saving and system throughput.