Many methods for inferring genetic regulatory networks have been proposed. However inferred networks can hardly be used to analyze the dynamics of genetic regulatory networks. Recently nonlinear differential equations are proposed to model genetic regulatory networks. Based on this kind of model, the stability of genetic regulatory networks has been intensively investigated. Because of difficulty in estimating parameters in nonlinear model, inference of genetic regulatory networks with nonlinear model has been paid little attention. In this paper, we present a method for estimating parameters in genetic regulatory networks with SUM regulatory logic. In this kind of genetic regulatory networks, a regulatory function for each gene is a linear combination of Hill form functions, which are nonlinear in parameters and in system states. To investigate the proposed method, the gene toggle switch network is used as an illustrative example. The simulation results show that the proposed method can accurately estimates parameters in genetic regulatory networks with SUM logic.