Abstract: The fast successive cancellation list (Fast-SCL) decoding algorithm for polar codes can achieve low latency, but still performs poorly under medium and short code lengths. To deal with this issue, this paper proposes an improved Fast-SCL algorithm by combining parity check (PC) and cyclic redundancy check (CRC). Specifically, PC bits are introduced into the Fast-SCL algorithm to enable real-time path verification, which makes the path selection more reliable. Additionally, with the same total number of check bits, various combinations of PC bits and CRC bits are considered. The simulation results demonstrate that the proposed algorithm achieves a performance gain of 0.35 dB and a complexity reduction of 10% compared to the original CRC-assisted Fast-SCL algorithm under the short code lengths with the frame error rate (FER) being 10^-2 .