Polar codes have become one of the most attractive topics in coding theory community because of their provable capacity-achieving property. Belief propagation (BP) algorithm, as one o f the popular approaches for decoding polar codes, has unique advantage of high parallelism but suffers from high computation complexity, which translates to very large silicon area and high power consumption. This paper, for the first time, exploits the design of polar BP decoder using stochastic computing. Several methods ranging from algorithm level to architecture level are presented to improve the error and hardware performances of the stochastic BP decoder. The approaches proposed in this work provide a potential low-cost solution for stochastic BP decoder design.