In the analysis of maximum-likelihood decoding performance of low-density parity-check (LDPC) codes, the weight distribution is an important factor. We presented a probabilistic method for computing the weight distribution of LDPC codes, and showed results of computing the weight distribution of several LDPC codes. In this paper, we improve our previously presented method and propose a probabilistic computation method with reliability for the weight distribution of LDPC codes. Using the proposed method, we can determine the weight distribution with small failure probability.