A method of decoding polar codes based on belief propagation includes conventional belief propagation to decode the polar codes first; when a number of iterations exceeds a predefined upper limit and a cyclic redundancy check fails, the method selects log-likelihood ratio vectors of a plurality of R or L messages from a plurality of log-likelihood ratio vectors generated in each of the iterations and generates another set of log-likelihood ratio vectors (referred to as candidate vector group) to be used as initial values of the R or L messages for a subsequent belief propagation to perform belief propagation decoding iterations and cyclic redundancy check again. Whenever a decoding result passes the cyclic redundancy check, the method exits; otherwise, the method iterates the above procedure until a maximum number of candidate vector groups has been reached.