Based on the random perturbation technique for reliability sensitivity design, some realistic reliability-based sensitivity issues are discussed, some of which have a structure of high nonlinear performance functions. Combining the related theories of the moment method of the reliability analysis, the matrix differential, and the Kronecker algebra, the reliability-based sensitivity method based on the perturbation method is modified if the first four moments of random variables are given. Meanwhile, a reliability-based sensitivity computation method is proposed. Some examples are used to show that using this method can effectively improve the accuracy of the reliability-based sensitivity computation and offer a reliable theoretic basis in engineering.