The issue of how to add transparency to artificial neural networks (ANNs) becomes more critical in machine learning. Rules extraction from neural network is well recognized to be an effective solution to dealing with this problem. This study focus on regression problems and aims to develop an algorithm to extract regression rules from ANNs. In order to extract a set of comprehensible and accurate regression rules, the intelligent algorithm of particle swarm optimization (PSO) is introduced in this paper. The main concepts are that use enough linear segments to approximate the nonlinear activation function of each hidden unit and replace them by integrating PSO and Least Squares (LS), where the PSO algorithm is applied to seek more linear segments and each linear segment is approximated by LS algorithm, then use the decision tree to generate regression rules from the approximated ANNs. The extracted linear regression rules not only ensure the accuracy but also enhance the explanation. Experiments on two benchmark datasets show that the proposed approach is more accurate than the existing approaches based on the decision tree or linear regression. Furthermore, the proposed algorithm can also be treated as an efficient algorithm for functions approximation with linear segments.