Normal transformation technique is often used in practical probabilistic analysis in structural or civil engineering especially when multivariate random variables with the probabilistic characteristics expressed using only statistical moments are involved. In this paper, a modified high-order moment method(MHOM) is given based on the polynomial coefficients of a third-order normal transformation polynomial (NTP) using the first four central moments of random variables having unknown distributions. The present high-order moment method is introduced into several typical test problems having unknown distributions are available. Since it needs neither the computation of derivatives nor iteration, and since it is unnecessary to know the probability distribution of the basic random variables, the present method should be practical in actual reliability problems. Applications to several typical examples have helped to elucidate the successful working of the present MHOM.