The optimization of trusses usually demands a number of structural analyses which leads to substantial computation cost and execution time, especially in case of large problems. Artificial Neural Networks (ANNs) have been proved as the effective surrogates for approximation of structural responses with acceptable accuracy and relatively low computational efforts. In this study, the efficacy of two different types of neural networks, Backpropagation Neural Network (BPNN) and Counterpropagation Neural Network (CPN), for the optimization of weights of truss structures is examined. The 52 membered space truss is used as the test problem where cross sections are used as the input data and the stresses of members as the outputs in order to train the neural networks. The performances of the models in respect of their accuracy and computational costs are investigated. It is found that whereas the backpropagation model performs better in respect of accuracy, the counterpropagation model performs much better in terms of the speed of the learning and computational costs. It is demonstrated that the proposed method is able to provide the capability of the surrogate modeling approach based on neural network models in accelerating the structural optimization process and minimizing the burden of the repetitive finite element.