Abstract: This paper shows how to construct generalized low-density (GLD) codes from Hamming-component product codes. Combining the decoding algorithms for linear block and LDPC codes，a novel Chase-MP algorithm for decoding of product codes is proposed by using the bipartite graph of the constructed sparse matrix. Since there are no cycles of length 4 or 6 in the graph, dependence among extrinsic information is greatly reduced during iterations and decoding performance is also improved. Experimental simulations for the (63,57,3)2 product code based on Hamming-component codes in terms of Bit Error Rate (BER) on the Additive White Gaussian Noise (AWGN) and Rayleigh fading channels show that our algorithm has remarkable coding gains. In comparison with the serially iterative Chase-2 algorithm, the Chase-MP algorithm is more convenient for fully parallelizable decoding and can achieve better performance.