Abstract For the detector in infrared focal plane arrays (IRFPA) with a large dynamic range of response, a nonlinear model of response curve of the detector in IRFPA is introduced in this paper. With the model, the Kalman-filter nonuniformity correction (NUC) algorithm with linear model, developed by Torres and Hayat, is extended. In the extended algorithm, the raw image is translated into a linearized one firstly by directly employing a logarithm-based transformation. Then the linearized image is corrected by the Kalman-filter NUC algorithm with linear model, and the corrected linearized image is obtained. Finally the uniformity image of the original one is achieved by fulfilling an exponent transformation to the corrected linearized image. The presented algorithm not only inherits the advantage of the original algorithm that resolves the problem of the temporal drift in the gain and the bias in each detector by updating NUC parameters with information of the current scene, but also reduce the influence of the detector nonlinear response to the NUC performance, so it is suitable for IRFPA under large response-range. The NUC ability of the presented algorithm is demonstrated by experiments with real infrared image sequences.