Spiking Neural Network (SNN) is considered more biologically plausible and energy-efficient on emerging neuromorphic hardware. Recently backpropagation algorithm has been utilized for training SNN, which allows SNN to go deeper and achieve higher performance. However, most existing SNN models for object recognition are mainly convolutional structures or fully-connected structures, which only have inter-layer connections, but no intra-layer connections. Inspired by Lateral Interactions in neuroscience, we propose a high-performance and noise-robust Spiking Neural Network (dubbed LISNN). Based on the convolutional SNN, we model the lateral interactions between spatially adjacent neurons and integrate it into the spiking neuron membrane potential formula, then build a multi-layer SNN on a popular deep learning framework, i.\,e., PyTorch. We utilize the pseudo-derivative method to solve the non-differentiable problem when applying backpropagation to train LISNN and test LISNN on multiple standard datasets. Experimental results demonstrate that the proposed model can achieve competitive or better performance compared to current state-of-the-art spiking neural networks on MNIST, Fashion-MNIST, and N-MNIST datasets. Besides, thanks to lateral interactions, our model processes stronger noise-robustness than other SNN. Our work brings a biologically plausible mechanism into SNN, hoping that it can help us understand the visual information processing in the brain.