Uncooled infrared images typically suffer from column fixed-pattern noise (FPN), which is introduced by the non-uniformity of the column-parallel readout circuit. It is a challenging task to remove column FPN without introducing stripe artifacts near strong vertical edges. In this paper, we introduce a novel single-frame-based algorithm to accurately correct column FPN. The algorithm contains two 1D filters. First, a 1D weighted least-squares filter is applied to perform edge-preserving filtering in the horizontal direction to obtain a coarse estimation of the clear scene. Then, a local weighted ridge regression is performed between the horizontal smoothed image and the raw infrared image in vertical direction to refine this estimation. Through an analysis on the cause of stripe artifacts, the proposed non-uniformity correction (NUC) algorithm is proved to be effective in eliminating this problem. The performance of our proposed algorithm is thoroughly investigated and compared to four state-of-the-art single-frame-based destriping methods using both simulated and real experiments.