A structural reliability analysis method is proposed to solve the issue of completely random missing input data in aerospace， vehicle and other engineering fields， with Yeo-Johnson transformation and maximum entropy principle. Firstly， the original data is transformed into normalized one by Yeo-Johnson transformation. Secondly， the size of data is enlarged by adding new samples generated by normal distribution. Then the Yeo-Johnson inverse transformation is derived and the augmented data is converted by it. Finally， the maximum entropy principle is used to determine the probability density function which is further used to calculate failure probability. The proposed method is applied to three illustrative examples. The results show that the proposed method can enlarge the total number of samples in missing data and solve the issue of completely random missing input data in structural reliability analysis. The proposed method has a feasibility and engineering application value.