This paper addresses the problem of separating audio sources from time-varying convolutive mixtures. We propose a probabilistic framework based on the local complex-Gaussian model combined with non-negative matrix factorization. The time-varying mixing filters are modeled by a continuous temporal stochastic process. We present a variational expectation-maximization (VEM) algorithm that employs a Kalman smoother to estimate the time-varying mixing matrix, and that jointly estimate the source parameters. The sound sources are then separated by Wiener filters constructed with the estimators provided by the VEM algorithm. Extensive experiments on simulated data show that the proposed method outperforms a block-wise version of a state-of-the-art baseline method.