Blind source separation (BSS) is a process to reconstruct source signals from the mixed signals. The standard BSS methods assume a fixed set of stationary source signals with the fixed distribution functions. However, in practical mixing systems, the source signals are nonstationary and temporally correlated; e.g. source signal may be abruptly active or inactive or even replaced by a new one. The mixing system is also time-varying. In this paper, we present a novel Gaussian process (GP) to characterize the time-varying mixing coefficients and the temporally correlated source signals. An online variational Bayesian algorithm is established to learn the noisy mixing process where GP priors are adopted to express the correlated sources as well as the mixing matrix. Experimental results demonstrate the effectiveness of proposed method in speech separation under different scenarios.