This paper proposes an alternative algorithm for the multi-channel variational autoencoder (MVAE), a recently proposed multichannel source separation approach. While MVAE is notable for its impressive source separation performance, its convergence-guaranteed optimization algorithm and the fact that it allows us to estimate source-class labels simultaneously with source separation, there are still two major drawbacks, namely, the high computational complexity and the unsatisfactory source classification accuracy. To overcome these drawbacks, the proposed method employs an auxiliary classifier VAE, which is an information-theoretic extension of the conditional VAE, for learning the generative model of the source spectrograms. Furthermore, with the trained auxiliary classifier, we introduce a novel algorithm for the optimization that can both reduce the computational time and improve the source classification performance. We call the proposed method fast MVAE (fMVAE) . Experimental evaluations revealed that fMVAE achieved source separation performance comparable to that of MVAE and a source classification accu-racy rate of about 80% while reducing computational time by about 93%.