Due to the advantages of parallel architecture and low power consumption, a field-programmable gate array (FPGA) is typically utilized as the hardware for convolutional neural network (CNN) accelerators. However, SRAM-based FPGA devices are extremely susceptible to single-event upsets (SEUs) induced by space radiation. In this paper, a fault tolerance analysis and fault injection experiments are applied to a CNN accelerator, and the overall results show that SEUs occurring in a control unit (CTRL) lead to the highest system error rate, which is over 70%. After that, a hybrid hardening strategy consisting of a finite state machine error-correcting circuit (FSM-ECC) and a triple modular redundancy automatic hardening technique (TMR-AHT) is proposed in this paper to achieve a tradeoff between radiation reliability and design overhead. Moreover, the proposed methodology has very small workload and good migration ability. Finally, by full exploiting the fault tolerance property of CNNs, a highly reliable CNN accelerator with the proposed hybrid hardening strategy is implemented with Xilinx Zynq-7035. When BER is 2 × 10−6, the proposed hybrid hardening strategy reduces the whole system error rate by 78.95% with the overhead of an extra 20.7% of look-up tables (LUTs) and 20.9% of flip-flops (FFs).