Abstract: Super-resolution image reconstruction has recently drawn considerable attention within the research area. For some special-purpose imaging devices such as medical imaging, remote sensor imaging and video capturing, the acquired images cannot often achieve a higher resolution because of the limitation of imaging mechanism and imaging sensor. Super-resolution image reconstruction methods attempt to create a single high-resolution and high-quality image from multiple low-resolution observations (or a video sequence) degraded by warping, blurring, noise and aliasing. So far, existing super-resolution methods are all confronted with the problem of slow convergence and expensive computation. To satisfy the requirement of real-occasion applications, a fast super-resolution reconstruction algorithm is built upon the MAP framework. In the proposed algorithm, two improvements are presented to reduce the high computational complexity of the standard MAP algorithm. The first improvement is to compute directly the increment of the MAP objective function as the component of the gradient vector, which avoids the redundant computation of the objective function. The second one is to select the Armijo rule to identify the step size, which avoids the computation of the computationally demanding Hessian matrix. Experimental results show that the computation time is reduced significantly, whereas the solutions convergence is guaranteed and the similar quality is maintained.