Radio astronomy image formation can be treated as a linear inverse problem. However, due to physical limitations, this inverse problem is ill-posed. To overcome the ill-posedness, side information should be involved. Based on the sparsity assumption of the sky image, we involve l1-regularization. We formulate the image formation problem into a l1-regularized weighted least square (WLS) problem and associate each variable with one regularization parameter. We use Bayesian learning to learn the regularization parameters from data by maximizing the posterior density. With the iterative update of the regularization parameters, the solution is updated until convergence of the regularization parameters. We involve a stopping rule based on the noise level to improve the computational efficiency and control the sparsity of the solution. We compare the performance of this Bayesian learning method with other existing imaging methods by simulations. Finally, we propose some future research directions in improving the performance of this Bayesian learning method.