Abstract: Belief Propagation (BP) decoding algorithm of Repeat Accumulate (RA) code approaches Shannon limit, but it possesses high complexity because of the use of the complex hyperbolic tangent function and the inverse hyperbolic tangent function at check nodes updating. In order to reduce the complexity with little performance sacrifice, combining the two methods lookup tables and piecewise approximation function, a modified decoding algorithm is proposed in this paper. The algorithm uses piecewise function to approximate the original function, which is obtained by transform and simplify the check node updating of BP algorithm, and use a very small lookup table to get a correction to correct error between the original function and approximate function. It can avoid the complex calculations, and get the minimal error. The algorithm greatly reduces the decoding complexity, and has a performance close to the BP decoding algorithm.