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With the rapid development of AI technology, we have witnessed numerous innovations and conveniences. However, along with these advancements come privacy threats and risks. Fully Homomorphic Encryption (FHE) emerges as a key technology for privacy-preserving computation, enabling computations while maintaining data privacy. Nevertheless, FHE has limitations in processing continuous non-polynomial functions as it is restricted to discrete integers and supports only addition and multiplication. Spiking Neural Networks (SNNs) operate on discrete spike signals, naturally aligning with the properties of FHE. In this paper, we present a framework called FHE-DiCSNN. This framework is based on the efficient TFHE scheme and leverages the discrete properties of SNNs to achieve high prediction performance on ciphertexts. Firstly, by employing bootstrapping techniques, we successfully implement computations of the Leaky Integrate-and-Fire neuron model on ciphertexts. Through bootstrapping, we can facilitate computations for SNNs of arbitrary depth. This framework can be extended to other spiking neuron models, providing a novel framework for the homomorphic evaluation of SNNs. Secondly, inspired by CNNs, we adopt convolutional methods to replace Poisson encoding. This not only enhances accuracy but also mitigates the issue of prolonged simulation time caused by random encoding. Furthermore, we employ engineering techniques to parallelize the computation of bootstrapping, resulting in a significant improvement in computational efficiency. Finally, we evaluate our model on the MNIST dataset. Experimental results demonstrate that, with the optimal parameter configuration, FHE-DiCSNN achieves an accuracy of 97.94% on ciphertexts, with a loss of only 0.53% compared to the original network's accuracy of 98.47%. Moreover, each prediction requires only 0.75 seconds of computation time