Multi-frame super-resolution focuses on reconstructing a high-resolution image from a set of low-resolution images with high similarity. The minimization function derived from maximum a posteriori probability (MAP) is composed of a fidelity term and a regularization term. In this paper, we propose a new fidelity term based on half-quadratic estimation to choose error norm adaptively instead of using fixed L1 or L2 norm. Besides, we propose a novel regularization method which combines the advantage of Difference Curvature (DC) and Bilateral Total Variation (BTV) to preserve the edge areas and remove noise simultaneously. The proposed framework is tested on both synthetic data and real data. Our experimental results illustrate the superiority of the proposed method in terms of edge preserving and noise removal over other state-of-the-art algorithms.