Based on univariate dimension reduction method（ UDRM）,edgeworth series and the relation of statistical moment,a method for calculation of failure probability of mechanical components is proposed. The univariate dimension reduction method is applied to calculate the response origin moments of fundamental input random variables. Edgeworth series is used to estimate failure probability of mechanical components by using first few response central moments. The non-normal random parameters need not to be transformed into equivalent normal ones. Two numerical examples are employed to illustrate the accuracy and efficiency of the proposed method and the second moment method by comparing the failure probability results.The results obtained by the proposed new method and the second moment method are compared with those obtained by Monte-Carlo Simulation（ MCS） respectively. The results show that the new method can calculate the failure probability of mechanical components effectively.