This paper proposes a low-complexity LDPC decoding algorithm with simplified check nodes updating. The proposed algorithm simplifies the result of the secondminimum in check nodes based on the first-minimum computation instead of computing it directly. In order to obtain the approximate result, effective corrected coefficients are utilized, which can reduce the complexity by eliminating the complex computations. Complexity analysis is provided and the results indicate that the complexity of the proposed algorithm is much lower than the general NMS algorithm and MS-based simplified algorithms. Simulation results show that the performance of the proposed algorithm can closely match the NMS algorithm with the same number of iterations.