Compressive sensing (CS)-based channel estimation considerably reduces pilot symbols usage by exploiting the sparsity of the propagation channel in the delay-Doppler domain. In this paper, we consider the application of Bayesian approaches to the sparse channel estimation in orthogonal frequency division multiplexing (OFDM) systems. Taking advantage of the block-sparse structure and statistical properties of time-frequency selective channels, the proposed Bayesian method provides a more efficient and accurate estimation of the channel status information (CSI) than do conventional CS-based methods. Moreover, our estimation scheme is not limited to the Gaussian scenario but is also available for channels that have non-Gaussian priors or unknown probability density functions. This characteristic is notably useful when the prior statistics of channel coefficients cannot be precisely estimated. We also design a combo pilot pattern to improve the performance of the proposed estimation scheme. Simulation results demonstrate that our method performs well at high Doppler frequencies.