Most recent infrared (IR) sensors have a focal-plane array (FPA) structure. Spatial non-uniformity of a FPA structure, however, introduces unwanted fixed pattern noise (FPN) to images. This non-uniformity correction (NUC) of a FPA can be categorized into target-based and scene-based approaches. In a target-based approach, FPN can be separated by using a uniform target such as a black body. Since the detector response randomly drifts along the time axis, however, several scene-based algorithms on the basis of a video sequence have been proposed. Among those algorithms, the state-of-the-art one based on Kalman filter uses one-directional warping for motion compensation and only compensates for offset non-uniformity of IR camera detectors. The system model using one-directional warping cannot correct the boundary region where a new scene is being introduced in the next video frame. Furthermore, offset-only correction approaches may not completely remove the FPN in images if it is considerably affected by gain non-uniformity. Therefore, for FPN reduction in IR videos, we propose a joint correction algorithm of gain and offset based on bi-directional warping. Experiment results using simulated and real IR videos show that the proposed scheme can provide better performance compared with the state-of-the art in FPN reduction.