This paper presents a new method for solving linear inverse problems where the observations are corrupted with a mixed Poisson-Gaussian noise. To generate a reliable solution, a regularized approach is often adopted in the literature. In this context, the optimal selection of the regularization parameters is of crucial importance in terms of estimation performance. The variational Bayesian-based approach we propose in this work allows us to automatically estimate the original signal and the associated regularization parameter from the observed data. A majorization-minimization technique is employed to circumvent the difficulties raised by the intricate form of the Poisson-Gaussian likelihood. Experimental results show that the proposed method is fast and achieves state-of-the art performance in comparison with approaches where the regularization parameters are manually adjusted.