When performing eye movement pattern classification for different tasks, support vector machines are greatly affected by parameters. To address this problem, we propose an algorithm based on the improved whale algorithm to optimize support vector machines to enhance the performance of eye movement data classification. According to the characteristics of eye movement data, this study first extracts 57 features related to fixation and saccade, then uses the ReliefF algorithm for feature selection. To address the problems of low convergence accuracy and easy falling into local minima of the whale algorithm, we introduce inertia weights to balance local search and global search to accelerate the convergence speed of the algorithm and also use the differential variation strategy to increase individual diversity to jump out of local optimum. In this paper, experiments are conducted on eight test functions, and the results show that the improved whale algorithm has the best convergence accuracy and convergence speed. Finally, this paper applies the optimized support vector machine model of the improved whale algorithm to the task of classifying eye movement data in autism, and the experimental results on the public dataset show that the accuracy of the eye movement data classification of this paper is greatly improved compared with that of the traditional support vector machine method. Compared with the standard whale algorithm and other optimization algorithms, the optimized model proposed in this paper has higher recognition accuracy and provides a new idea and method for eye movement pattern recognition. In the future, eye movement data can be obtained by combining it with eye trackers to assist in medical diagnosis.