A fundamental and important approach in the field of seismic signal processing is the deconvolution of seismic signals. However, seismic signal acquisition can be contaminated by outliers, and the outliers affect the performance of deconvolution results. In this paper, we follow the Bayesian deconvolution framework, which was proposed by Canadas, and propose a new robust sparse deconvolution method for overcoming the influence of outliers. The new approach properly models the heavy-tail outliers and sparse reflection coefficients simultaneously. For solving the approach, we derive a type of alternative algorithm. Finally, we demonstrate the performance of the algorithm by a series of simulations, which show that the new approach can eliminate the influence of heavy-tail outliers and recover the reflection coefficients. This further indicates the approach is valid and the algorithm is convergent.