In multi-view environment, it would yield missing observations due to the limitation of the observation process. The most current representation learning methods struggle to explore complete information by lacking either cross-generative via simply filling in missing view data, or solidative via inferring a consistent representation among the existing views. To address this problem, we propose a deep generative model to learn a complete generative latent representation, namely Complete Multi-view Variational Auto-Encoders (CMVAE), which models the generation of the multiple views from a complete latent variable represented by a mixture of Gaussian distributions. Thus, the missing view can be fully characterized by the latent variables and is resolved by estimating its posterior distribution. Accordingly, a novel variational lower bound is introduced to integrate view-invariant information into posterior inference to enhance the solidative of the learned latent representation. The intrinsic correlations between views are mined to seek cross-view generality, and information leading to missing views is fused by view weights to reach solidity. Benchmark experimental results in clustering, classification, and cross-view image generation tasks demonstrate the superiority of CMVAE, while time complexity and parameter sensitivity analyses illustrate the efficiency and robustness. Additionally, application to bioinformatics data exemplifies its practical significance.