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The successive cancellation(SC) decoding method for polar codes under additive white Gaussian noise (AWGN) channels is performed in the log-likelihood ratio(LLR) domain. The calculation of the f function nodes use a sum-product algorithm based on hyperbolic tangent rules. This paper proposed a polyline approximation algorithm, which simplified the hyperbolic tangent function and the inverse hyperbolic tangent function into a 9-segment polyline function respectively. In order to obtain better FER performance under the polyline approximation algorithm, this algorithm added a 16 bit CRC to the information bits before encoding. Simulation experiments show that for the polar codes with code length N = 1 024 and information bit length K = 496, the proposed algorithm has better FER performance than the sum-product algorithm, and it reduces the decoding complexity and improves the decoding speed. [ABSTRACT FROM AUTHOR]