The intershaft bearing is located between the high and low-pressure rotors of the aero-engine, where the working environment is harsh, the load variation range is large, and the lubrication and heat dissipation are poor. The fault of the intershaft bearing is sudden and will cause the engine to hold the shaft and break the shaft, which is more harmful than the ordinary bearings. In recent years, bearing intelligent fault diagnosis methods based on deep learning have been widely applied. However, most of the existing methods are mainly proposed based on second-generation neural networks. Spiking neural network (SNN), also known as the third-generation neural network, mimics the dynamics of the biological brain and is more powerful for processing time-series information. As we know, vibration data is a typical time-series data, SNN would have stronger feature extraction potential for it. In this paper, we propose an improved spiking neural network (ISNN) for intershaft bearing fault diagnosis. Specifically, we propose an encoding method to encode raw data into spike sequences and demonstrate that the encoding method is accurate and efficient. Then we derive the gradient relation in the ISNN and mathematically prove the replacement of invalid gradients in it. Furthermore, we compensate for the loss of information in forward propagation and simplify the process of backpropagation by constructing suitable spiking neurons. Finally, we test the ISNN on the fault dataset of intershaft bearings, and the results show that the proposed ISNN outperforms previous SNNs and typical second-generation neural networks.