This paper proposes a hybrid approach combining Recurrent Neural Network (RNN) and polynomial regression methods for time-domain modeling of nonlinear circuits. The proposed hybrid RNN-polynomial regression (HRPR) method merges RNN and polynomial regression which leads to a significant reduction in training time while providing speedup in simulation compared to both conventional RNN and existing models in simulation tools without sacrificing accuracy. The proposed HRPR method comprises two steps: First, an RNN structure is generated, and then, the output of the RNN is combined with external input(s) of the circuit to perform a regression. Applying this method causes part of the training process to be done by polynomial regression which is simpler than training an RNN. Also, the RNN used in the HRPR method has a simpler structure than a single conventional RNN used for modeling the same component. To verify the validity of the proposed method, modeling and comparisons of three nonlinear examples are presented in this paper.