Channel state information (CSI) is required at receiver in orthogonal frequency division modulation (OFDM) communication systems due to the fact that frequency-selective fading channel leads to inter-symbol interference (ISI) over data transmission. Broadband channel model is often described by very few dominant channel taps and they can be probed by sparse channel estimation (SCE) methods, e.g., subspace pursuit (SP) algorithm, can take the advantage of sparse structure effectively in broadband channels as for prior information. However, these developed methods are vulnerable to both noise, interference and column coherence of training signal matrix. In other words, the primary objective of these conventional methods is to catch the dominant channel taps without a report of posterior channel uncertainty. To improve the estimation performance, we proposed a Bayesian sparse channel estimation (BSCE) method which not only exploits the channel sparsity but also mitigates the unexpected channel uncertainty. The proposed method can reveal potential ambiguity among multiple channel estimators that are ambiguous due to observation noise or correlation interference among columns in the training matrix. Computer simulations show that our technique can improve the estimation performance with comparable computational complexity when comparing with conventional SCE methods.