A critical problem of maximum a posteriori (MAP) super-resolution (SR) image reconstructed algorithms is the choice of an appropriate prior model. Instead of modeling an original image directly, this work proposes an edge-image-based approach for stable SR reconstruction of the Lorentzian distribution. Through analyzing the convex and derivative properties of the Lorentzian distribution, we demonstrate the validity and stability of the proposed method for MAP SR reconstruction. The Lorentzwidth parameter is calculated iteratively to control the general sharpness degree of the image in the SR reconstruction process. Experiments confirm the effectiveness and robustness of the proposed method, and yield both objective and subjective qualities of the reconstructed SR images significantly better than conventional methods.