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The first-order grey model is appropriate for monotonic time series, while the grey Verhulst model is appropriate for periodic time series. The grey Verhulst model is widely used for predicting practical nonlinear time series that contain fluctuations. Despite the successful application of the grey models in practice, researchers show that grey models still have room for improvement. Moreover, recent research shows that grey models are sensitive to initial conditions. In many practical problems, the value of initial conditions is not accurate and suffers from noise or approximation errors, resulting in inaccurate prediction. To address these difficulties, an improved grey Verhulst method using particle swarm optimization is proposed in this paper. The proposed model consists of two stages. In the first stage, a second-order polynomial with unknown coefficients is used to approximate the 1- AGO. In the second stage, the initial element of the time series is modified to improve the accuracy of the prediction. The particle swarm optimization method is used to search for the unknown coefficients. It is found that PSO is a suitable optimization method for the proposed method because it is stable and generates a sequence of points that converges to a globally optimal solution. To demonstrate the efficiency and stability of the proposed method, it was applied to five practical problems, namely, gas production in China, the number of hazardous chemical accidents, CO2 emissions in Russia, the number of domestic tourists in China, and traffic flows in Canada. Numerical results show that the method is more accurate and robust than existing methods. • The proposed method needs only four elements for predicting the future elements of time series. • The paper proposes a second order polynomial for approximating 1-AGO. • The method makes more accurate prediction than existed methods. • The proposed method is applied on various practical forecasting problems successfully. [ABSTRACT FROM AUTHOR]