Low density parity check code (LDPC) is a widely used channel coding, especially in long code. Corresponding to coding is decoding. The complexity of traditional LDPC decoding algorithm is high. Approximate operation has been adopted in the minimum sum (MS) decoding algorithm to reduce the complexity. Although the complexity can be effectively reduced, some BER performance is sacrificed. In view of the problem, we proposed a class fitting modified minimum sum (CFMMS) decoding algorithm, which performs the approximate operation for a second time based on the MS decoding algorithm. The algorithm constructs a fitting function according to the nonlinear function in MS algorithm, which can make different processing for the variable node information in different thresholds, and achieve accurate compensation for the updating process of verification nodes, so that the obtained results are closer to the confidence propagation algorithm. On the basis of the hierarchical scheduling strategy, a layered class fitting modified minimum sum (LCFMMS) decoding algorithm was proposed, which can change the update order of node information, improve the reliability of node information in iterative update, accelerate the convergence speed of decoding, and save storage space. Simulation and numerical results show that the proposed decoding algorithm improved bit-error rate (BER) performance to a certain extent, and had low computational complexity and fast decoding convergence speed.