In scene-based nonuniformity correction (NUC) methods for infrared focal plane array cameras, the statistical approaches have been well studied because of their lower computational complexity. However, when the assumptions imposed by statistical algorithms are violated, their performance is poor. Moreover, many of these techniques, like the global constant statistics method, usually need tens of thousands of image frames to obtain a good NUC result. In this paper, we introduce a new statistical NUC method called the multiscale constant statistics (MSCS). The MSCS statically considers that the spatial scale of the temporal constant distribution expands over time. Under the assumption that the nonuniformity is distributed in a higher spatial frequency domain, the spatial range for gain and offset estimates gradually expands to guarantee fast compensation for nonuniformity. Furthermore, an exponential window and a tolerance interval for the acquired data are introduced to capture the drift in nonuniformity and eliminate the ghosting artifacts. The strength of the proposed method lies in its simplicity, low computational complexity, and its good trade-off between convergence rate and correction precision. The NUC ability of the proposed method is demonstrated by using infrared video sequences with both synthetic and real nonuniformity.