A higher moment method with the basis of Chebyshev polynomial { T_k(x)} is presented, which is used in the reliability analysis of engineering structures. The equations of optimal probability density function of stochastic variable or limit state function are derived by use of the higher moments of the function. Subsequently, a reliability index or failure probability of the engineering structures can be calculated. From the comparison of the classical distribution function and the failure probability for the components, this method is proved to be valuable and practicable in engineering application.