Seasonality is a fundamental and common property of most time series in the real world. In this article, we propose a grey seasonal least square support vector regression, abbreviated as GSLSSVR, by combining the dummy variables, framework of the LSSVR model, and grey accumulation generation operation to reflect seasonal variations in functional forms, variables, and parameters. Our framework provides an intuitive and simple set up of arbitrary seasonality in any feature, which considerably enhances model realism. Further, the regulation method is introduced to increase the stability and generalization of the newly proposed model. Using the Lagrange multipliers algorithm, the model parameters are obtained by solving a set of linear equations. In addition, the last block evaluation is developed, which has the same size in the validating and testing data, to identify the hyperparameters of this novel model. For verification purposes, four real seasonal time series having various characteristics are employed in this work, including quarterly electricity consumption, monthly cargo throughput, monthly crude oil production, and monthly gasoline production in China. Experimental results demonstrate that our proposed model can provide for analysis of seasonal regulatory measures and is validated to be superior to other prevalent forecasting models referring to the SGM(1,1), SFGM(1,1), LSSVR, SARIMA-GARCH, and BPNN models. Ultimately, our model is highly recommended for addressing issues with periodic and nonlinear features.