An improved successive cancellation list bit-flip based on assigned set (AS-SCLF) decoding algorithm is proposed to solve the problems that the successive decoding of the successive cancellation (SC) decoder has error propagation and the path extension of the successive cancellation list (SCL) decoder has the decision errors in the traditional cyclic redundancy check aided successive cancellation list (CA-SCL) decoding algorithm. The proposed algorithm constructs the AS firstly. The construction criterion is to use the Gaussian approximation principle to estimate the reliabilities of the polar subchannel and the error probabilities of the bits under SC decoding, and the normalized beliefs of the bits in actual decoding are obtained through the path metric under CA-SCL decoding, thus the error bits containing the SC state are identified and sorted in ascending order of the reliability. Then the SCLF decoding is performed. When the CA-SCL decoding fails for the first time, the decision results on the path of the SC state in the AS are exchanged. The simulation results show that compared with the CA-SCL decoding algorithm, the SCLF decoding algorithm based on the critical set and the decision post-processing decoding algorithm, the improved AS-SCLF decoding algorithm can improve the gain of about 0.29 dB, 0.22 dB and 0.1 dB respectively at the block error rate (BLER) of 10-4 and reduce the number of decoding at the low signal-to-noise ratio (SNR), thus the computational complexity is also reduced.