For resolving the influence that the nonlinear response of detectors imposed on the nonuniformity correction (NUC) for infrared focal plane arrays, a new improved Kalman-filtering nonuniformity correction algorithm with a nonlinear model is presented. In this algorithm, the nonlinear image data is translated into linearized one firstly, then the Kalman-filter NUC algorithm with a linear model is utilized to correct nonuniformity of the linearized image. Finally the exponents of the corrected linearized image data is calculated, and the uniformity image of the original one is achieved. Experimental results indicate that the presented algorithm not only inherits the advantage of the original algorithm, which resolves the problem of detector offset and gain drift with time by updating NUC parameters with information of the current scene, but also reduces the influence of the detector nonlinear response to the NUC performance in some degree, and acquires good NUC effect.