In this paper we propose the Gaussian sum resampling filter (GSRF) in which the predicted state distribution is approximated by the sum of the sub-Gaussian components whose variances are designed to be smaller than the Gaussian components used for the standard Gaussian sum filter (GSF). These sub-Gaussian components contribute for the improvement in the subsequent Gaussian sum approximation of the filtered state distribution and the diversity produced in the sub components also work for the enhancement of the state estimation accuracy. The resampling of the sub components makes the number of the Gaussian components constant throughout the filter execution. Numerical examples show the superior filtering accuracy of the GSRF over the other existing filters including the GSF.