In recent years, studies on image generation models of spiking neural networks (SNNs) have gained the attention of many researchers. Variational autoencoders (VAEs), as one of the most popular image generation models, have attracted a lot of work exploring their SNN implementation. Due to the constrained binary representation in SNNs, existing SNN VAE methods implicitly construct the latent space by an elaborated autoregressive network and use the network outputs as the sampling variables. However, this unspecified implicit representation of the latent space will increase the difficulty of generating high-quality images and introduces additional network parameters. In this paper, we propose an efficient spiking variational autoencoder (ESVAE) that constructs an interpretable latent space distribution and design a reparameterizable spiking sampling method. Specifically, we construct the prior and posterior of the latent space as a Poisson distribution using the firing rate of the spiking neurons. Subsequently, we propose a reparameterizable Poisson spiking sampling method, which is free from the additional network. Comprehensive experiments have been conducted, and the experimental results show that the proposed ESVAE outperforms previous SNN VAE methods in reconstructed & generated images quality. In addition, experiments demonstrate that ESVAE's encoder is able to retain the original image information more efficiently, and the decoder is more robust. The source code is available at https://github.com/QgZhan/ESVAE.