Finding the optimal design parameters for the target EM response of a metamaterial absorber is still a challenging task even if the layout of the absorber has been determined. To effectively address this issue, we introduce the idea of surrogate-based optimization into the area of metamaterial absorber design. This paper proposes a surrogate based optimization method combining artificial neural network (ANN) and trust region algorithm for metamaterial absorbers. Each optimization iteration utilizes the optimal solution from the previous iteration and the sample points surrounding it as the training dataset to build an effective ANN surrogate model. To improve the convergence of the optimization method for metamaterial absorbers based on ANN surrogate model, we incorporate a trust region algorithm. The proposed method employs a simple forward neural network architecture and requires less training data, leading to a quick convergence towards the target solution after only a few iterations. Compared to the three commonly used alternative methods, the proposed method can optimize geometric and material parameters more efficiently in the same time. The validity of the proposed method is demonstrated by two examples of electromagnetic optimizations of metamaterial absorbers.