Obtaining the downlink channel state information in frequency division duplexing (FDD) massive multi-input multi-output (MIMO) systems is challenging due to the overwhelming training and feedback overhead. In this letter, motivated by the existence of mapping characteristics between uplink and downlink, we propose a covariance variational auto-encoder network (CVENet) to approximate the mapping function. Different from normal auto-encoder, the CVENet extracts the uplink channel covariance to a latent distribution space and then predicts the downlink channel covariance by the sample of the space. Simulation results demonstrate that the CVENet performs better than the conventional dictionary pairs algorithm. And the CVENet still achieves robustness in a circumstance where the channel environment of the training stage is different from the deployment stage, which shows its practical applicability.