Prior works typically conducted the fault analysis of neural network accelerator computing arrays with simulation and focused on the prediction accuracy loss of the neural network models. There is still a lack of systematic fault analysis of the neural network acceleration system that considers both the accuracy degradation and system exceptions, such as system stall and running overtime. To that end, we implemented a representative neural network accelerator and corresponding fault injection modules on a Xilinx ARM-FPGA platform and evaluated the reliability of the system under different fault injection rates when a series of typical neural network models are deployed on the neural network acceleration system. The entire fault injection and reliability evaluation system is open-sourced on GitHub. With comprehensive experiments on the system, we identify the system exceptions based on the various abnormal behaviors of the FPGA-based neural network acceleration system and analyze the underlying reasons. Particularly, we find that the probability of the system exceptions dominates the reliability of the system. The faults also incur accuracy degradation of the neural network models, but the influence depends on the applications of the models and can vary greatly. In addition, we also evaluated the use of conventional triple modular redundancy (TMR) and demonstrated the challenge of TMR with both experiments and analytical models, which may shed light on the reliability design of the FPGA-based neural network acceleration system.