Symbolic propagation methods based on linear abstraction play a significant role in neural network verification. This paper proposes the notion of multi-path back-propagation for such methods. Existing methods are viewed as using only a single back-propagation path to calculate the upper and lower bounds of each node in a given neural network, so they are specific instances under the proposed notion. Leveraging multiple back-propagation paths effectively improves the accuracy of this kind of methods. For evaluation, the proposed multi-path back-propagation method is quantitatively compared with the state-of-the-art tool DeepPoly on benchmarks ACAS Xu, MNIST, and CIFAR10. The experiment results show that the proposed method achieves significant accuracy improvement while introducing only a low extra time cost. In addition, the multi-path back-propagation method is compared with the Optimized LiRPA, a tool based on global optimization, on the dataset MNIST. The results show that the proposed method still has an accuracy advantage.