Abstract The structure defect of the traditional grey Verhulst model is a key factor leading to its unstable performance. A new-structure grey Verhulst model (N_Verhulst) was proposed by introducing a new non-homogeneous exponential function. The N_Verhulst model has a better structure and stronger modeling ability; Meanwhile, it overcomes the shortcomings of the traditional Verhulst model including parameter dislocation and unreasonable selection of initial values. Four typical cases were used to test the performance of N_Verhulst, and the simulation/prediction results of the new model were compared with the traditional Verhulst model and the Pearl model. Results showed that the N_Verhulst model had evidently superior performance to the traditional grey Verhulst model, which confirms that the structure development of the new model is reasonable and effective.