Some optimization problems in the practical engineering and controlling fields are normally computationally expensive, which limits the application of evolutionary algorithms for solving these problems because a number of objective evaluations are often required before locating at the optimal solution. The utilization of surrogate models to assist evolutionary algorithms is efficient for solving computationally expensive problems. However, the sampling method, which is used to select solutions to be evaluated using the exact time-consuming objective function, plays a key role to obtain a good performance of the surrogate-assisted evolutionary algorithm. In this paper, the radial basis function network is adopted as the surrogate model, and a new method to evaluate the uncertainty of the approximated value is proposed. Then, a new sampling strategy is given based on the approximation uncertainty and approximated value to adaptively select solutions for exact objective evaluation, which can assist the algorithm to find a better solution in a limited number of objective evaluations. The performance of the proposed method is verified by comparing to some state-of-the-art algorithms published in recent years on seven test problems with a maximum of $100$ dimensions. The experimental results show that the proposed method can get better results in the same number of objective evaluations.