Accurately estimating correlation between sources has significant impact on the performance of Slepian-Wolf (SW) coding. In this paper, we propose a low complexity estimator based on Laplace propagation for exploiting the source correlation at the decoder side, by modeling the correlation estimation as a Bayesian inference problem. Through simulations, we show that the proposed algorithm can simultaneously reconstruct a compressed source and estimate both stationary and time-varying joint correlation between the sources at the bit level. Furthermore, comparing to the conventional SW decoder, the proposed approach can achieve a better decoding performance under varying correlation statistics and the proposed estimator shows a very fast convergence speed and low complexity compared with state-of-the-art sampling approaches.