A novel moment method is proposed to predict the detailed size distribution for particle coagulation. The method uses the log skew normal distribution (LSND) to approximate the actual size distribution. The LSND is a four-parameter distribution that generalizes the conventional log-normal distribution to allow for asymmetrical characteristics. The moment closure is achieved by applying the Gauss-Hermite quadrature for the integral terms in the moment equations. With this approach, no further treatments are needed for specific coagulation kernels. Then the method is validated by comparing it with other recognized numerical methods for Brownian coagulation in the continuum regime and the free-molecular regime. The results show that the present method well predicts the detailed size distribution over the entire coagulation time for both regimes. Moreover, the tails of the self-preserving size distribution are well reproduced by the present method. The asymptotic characteristics of Brownian coagulation are also analyzed based on the LSND. The results validate the LSND in analytically representing the self-preserving size distribution and predicting the asymptotic geometric standard deviation.