Because the application of statistical tolerance can reduce manufacturing costs while improving the quality of product,it is widely used in manufacturing industry.In statistical tolerance analysis and synthesis,it is usually assumed that the statistical tolerance is normally distributed.But in practice,there are many non-normal distributions in industrial production,such as uniform distribution,triangular distribution,et al.In order to analyze non-normal distributions,the simplest way is to transform non-normal distribution into normal distribution.But the accuracy of this way is a low.Monte-Carlo simulation can analyze non-normal distribution,but it is time consumed and inefficient.Convolution method is an accurate method to analyze statistical tolerance,but there are few studies about it because of the difficulty.In this paper,analytical convolution method is used to resolve non-normal distribution,and the probability density functions of closed loop in dimension chain are obtained.Comparing with Monte-Carlo simulation and moment methods,convolution method is faster and has better accuracy.Based on the method proposed in this paper,it is feasible to make computer-aided statistical tolerance analysis using convolution method.