In this letter, the principle of LLR-based successive-cancellation (SC) polar decoding algorithm is explored. In order to simplify the logarithm and exponential operations in the updating rules for polar codes, we further utilize a piece-wise linear algorithm to approximate the transcendental functions, where the piece-wise linear algorithm only consists of multiplication and addition operations. It is demonstrated that with one properly allowable maximum error δ chosen for success-failure algorithm, performances approach to that of the standard SC algorithm can be achieved. Besides, the complexity reduction is realized by calculating a linear function instead of nonlinear function. Simulation results show that our proposed piece-wise SC decoder greatly reduces the complexity of the SC-based decoders with no loss in error correcting performance.