In order to solve the problems of slow convergence speed and low optimization accuracy in whale optimization algorithm, a whale optimization algorithm based on iterative mapping and nonlinear fitting（NWOA） is proposed. Firstly, iterative mapping is taken advantage to initialize whale population, which guarantees initial population diversity. Secondly, nonlinear fitting strategy is used to improve the convergence factor and inertia weight to balance the global survey ability and local development ability of the algorithm. Through the simulation test of 13 functions , the improved algorithm has a significant improvement in precision and stability from the point of mean square error and average value. The experimental results show that the convergence speed of the algorithm is faster than that of the traditional whale optimization algorithm.