An adaptive surrogate model based on iteration sampling and extended radial basis function is proposed. The purpose of this adaptive method is reducing the number of simulation calculations and improving the surrogate model adaptive ability by multi-island GA algorithm. New sample points are located in the blank area and all the sample points are distributed in the design space uniformly. The precision of the surrogate model is checked using standard error measure to judge whether updating the surrogate model or not. Multi-island GA algorithm is combined with the adaptive surrogate model to find the optimum modal characteristic of an inertial sensor structure for electric helicopters. A total of ten training points are selected to construct the initial surrogate model using Latin hypercube sampling (LHS). The results of adaptive surrogate model show that seven new sampling points are needed to improve the accuracy of the surrogate model under the condition of 2% confidence bounds. The optimization results show that the selection of the weights for the objective functions will have a significant effect on the final optimum modal characteristic. And the optimization results indicate that the optimum modal characteristic makes the natural frequency away from the excitation frequency.