Existing decoding algorithms for polar codes still suffer from very high complexity. To solve this problem, an SCL decoding algorithm based on BP neural network is proposed. In offline, the algorithm builds and trains an appropriate BP neural network by collecting data. With the trained BP neural network, the optimal initial value of list size L is found through on-line operation. On this basis, the complexity is reduced by designing an improved SCL decoding algorithm. Experimental results show that compared with existing algorithms, the proposed algorithm can significantly reduce the average decoding complexity at low SNR.