Abstract: The current power analysis attack of SM4 belongs to the single point power analysis attack. The single point power analysis attack does not use all the information related with the key in the algorithm and the single power trace. There are two limitations with the single point power analysis attack: it needs more power traces when SM4 is attacked, and the information utilization rate of the attack is low. To solve the questions of the attack, a novel method of multi-point joint power analysis attack of SM4 is proposed in this paper. Multiple information leakage points related with the key are selected at the same time. Multi-point joint power leakage function is constructed by the intermediate variable of the information leakage points and the power leakage model. The key of SM4 is attacked out by the proposing attack. The experiments demonstrate the effectiveness of the proposed attack method, and comparing with the single point power analysis attack method, the proposed attack method can improve the attack success rate, reduce the number of the attack traces, and improve the energy efficiency of the attack. According to the characteristics of the proposed method, it can also be applied to the power analysis attacks of the other cryptographic algorithms.