This paper introduces a new intelligent optimization algorithm, named Firework Algorithm (FWA), to optimize the parameter selection process in the Support Vector Regression model (SVR). And then, considering the seasonal factors in tourism economic behavior, we build a seasonally-adjusted FWA-SVR model and apply it to predict the number of overnight tourists and tourism revenue of Hainan International Tourism Island. The prediction results show that the FWA-SVR model after the seasonal adjustment has better prediction accuracy than the ARMA model without seasonal adjustment. Compared with the classic Genetic Algorithm and Particle Swarm Optimization Algorithm, the FWA-SVR model performs best in all prediction models.