Collaborative Filtering (CF) is one of the most used methods for Recommender System. Because of the Bayesian nature and nonlinearity, deep generative models, e.g. Variational Autoencoder (VAE), have been applied into CF task, and have achieved great performance. However, most VAE-based methods suffer from matrix sparsity and consider the prior of users' latent factors to be the same, which leads to poor latent representations of users and items. Additionally, most existing methods model latent factors of users only and but not items, which makes them not be able to recommend items to a new user. To tackle these problems, we propose a Neural Variational Hybrid Collaborative Filtering, NVHCF. Specifically, we consider both the generative processes of users and items, and the prior of latent factors of users and items to be side informationspecific, which enables our model to alleviate matrix sparsity and learn better latent representations of users and items. For inference purpose, we derived a Stochastic Gradient Variational Bayes (SGVB) algorithm to analytically approximate the intractable distributions of latent factors of users and items. Experiments conducted on two large datasets have showed our methods significantly outperform the state-of-the-art CF methods, including the VAE-based methods.