Super-resolution is a technique to remove the noise of observed images and restore its high frequencies. We focus on reconstruction-based super-resolution. Reconstruction requires large computation cost since it requires many images. In this paper, we propose a fast weighted adder for reconstruction-based super-resolution. From the viewpoint of reducing partial products, we propose two approaches to speed up a weighted adder. First, we use selector logics to halve its partial products. Second, we propose a weights-range limit method utilizing negative term. By applying our proposed approaches to a weighted adder, we can reduce carry propagations and our weighted adder can be designed by a fast circuit as compared to conventional ones. Experimental evaluations demonstrate that our weighted adder improves the performance by a maximum of 29.9% and reduces a maximum of 592 LUTs, compared to conventional implementations.