It is well-known that the fatigue lives of metal material have a considerable amount of scatter and they are commonly suggested to be considered in engineering design. A rational computational method is proposed for identifying the probability distribution of fatigue life in this paper, in order to reduce the introduction of subjective uncertainties and obtain rational probability distribution. Firstly the sample statistics are used to estimate the first four statistical moments of fatigue life. Then, based on all those statistical moment constraints, the maximum entropy principle is employed to identify a rational probability distribution for fatigue life of interest. An accurate algorithm based on optimization theory is also presented to find the Lagrange multipliers in maximum entropy distribution, which can avoid the numerical singularity when solving a system of equations. The rationality and effectiveness of the proposed method are demonstrated by the experimental data of 2024-T351 aluminum alloy specimens available in the literature.