Abstract: A type of inexact adaptive finite element method for semilinear elliptic problems is considered. The algorithm needs an accurate solution on the coarsest level, and the remaining levels involve only single Newton updates to the previous approximate solution. By using the super approximation property between the exact and inexact solutions of finite element method, the priori and posteriori error estimates of the proposed method are given, and the numerical experiments are provided to illustrate the theory and the algorithm.