We develop a novel MRI reconstruction algorithm with an edge-preserving filtering prior. In the proposed algorithm, a gradient domain guided image filtering (GGF) is embedded into a commonly-used MRI reconstruction method, which can promote image structures and suppress artifacts or noise. And the l₁ norm is accurately imposed on the GGF prior which measures the error between guidance and ideal images in gradient domain. We first turn the MRI reconstruction problem into a two-phase objective function, and then we derive an efficient optimization scheme to address the proposed model by iteratively alternating GGF and l₁ norm approximations, and guidance and ideal images reconstructions. We finally provide numerous experiments to validate the effectiveness of the proposed method in both noise-free and noisy MRI reconstructions, and the proposed method outperforms several leading reconstruction approaches in both subjective results and objective assessments. In addition, our method can be effective in computed tomography (CT) image reconstruction.