To increase the accuracy of R-F method, it is necessary to solve the problems of the linear expansion of failure function and non-normal variables. In this paper, the improved FOSM method was applied to calculate the failure probability of welded pipes with cracks. The examples show that this method is simple, efficient and accurate for reliability safety assessment of welded pipes with cracks. It can save more time than the Monte Carlo method does, so that the improved FOSM method is recommended for general engineering reliability safety assessment of welded pipes with cracks.