In this paper, we present an iterative method based on gradient maximal convergence rate to compute Moore--Penrose inverse $A^\dag$ of a given matrix $A$. By this iterative method, when taken the initial matrix $X_0=A*$, the M-P inverse $A^\dag$ can be obtained with maximal convergence rate in absence of roundoff errors. In the end, a numerical example is given to illustrate the effectiveness, accuracy and its computation time, which are all superior than the other methods for the large singular matrix.