Large-scale neuromorphic dataset is costly to construct and difficult to annotate because of the unique high-speed asynchronous imaging principle of bio-inspired cameras. Lacking of large-scale annotated neuromorphic datasets has significantly hindered the applications of bio-inspired cameras in deep neural networks. Synthesizing neuromorphic data from annotated RGB images can be considered to alleviate this challenge. This paper proposes a simulator to generate simulated spiking data from images recorded by frame cameras. To minimize the deviations between synthetic data and real data, the proposed simulator named SpikingSIM considers the sensing principle of spiking cameras, and generates high-quality simulated spiking data, e.g., the noises in real data are also simulated. Experimental results show that, our simulator generates more realistic spiking data than existing methods. We hence train deep neural networks with synthesized spiking data. Experiments show that, the network trained by our simulated data generalizes well on real spiking data. The source code of SpikingSIM is available at http://github.com/Evin-X/SpikingSIM.