Spiking neural networks provide an alternative solution to conventional artificial neural networks with energy-saving and high-efficiency characteristics after hardware implantation. However, due to its non-differentiable activation function and the temporally delayed accumulation in outputs, the direct training of SNNs is extraordinarily tough even adopting a surrogate gradient to mimic the backpropagation. For SNN training, this non-differentiability causes the intrinsic gradient error that would be magnified through layerwise backpropagation, especially through multiple layers. In this paper, we propose a novel approach to reducing gradient error from a new perspective called surrogate module learning (SML). Surrogate module learning tries to construct a shortcut path to back-propagate more accurate gradient to a certain SNN part utilizing the surrogate modules. Then, we develop a new loss function for concurrently training the network and enhancing the surrogate modules' surrogate capacity. We demonstrate that when the outputs of surrogate modules are close to the SNN output, the fraction of the gradient error drops significantly. Our method consistently and significantly enhances the performance of SNNs on all experiment datasets, including CIFAR-10/100, ImageNet, and ES-ImageNet. For example, for spiking ResNet-34 architecture on ImageNet, we increased the SNN accuracy by 3.46%.