Extraction and analysis of electroencephalogram (EEG) signal characteristics of patients with autism spectrum disorder (ASD) is of great significance for the diagnosis and treatment of the disease. Based on recurrence quantitative analysis (RQA)method, this study explored the differences in the nonlinear characteristics of EEG signals between ASD children and children with typical development (TD). In the experiment, RQA method was used to extract nonlinear features such as recurrence rate (RR), determinism (DET) and length of average diagonal line (LADL) of EEG signals in different brain regions of subjects, and support vector machine was combined to classify children with ASD and TD. The research results show that for the whole brain area (including parietal lobe, frontal lobe, occipital lobe and temporal lobe), when the three feature combinations of RR, DET and LADL are selected, the maximum classification accuracy rate is 84%, the sensitivity is 76%, the specificity is 92%, and the corresponding area under the curve (AUC) value is 0.875. For parietal lobe and frontal lobe (including parietal lobe, frontal lobe), when the three features of RR, DET and LADL are combined, the maximum classification accuracy rate is 82%, the sensitivity is 72%, and the specificity is 92%, which corresponds to an AUC value of 0.781. The research in this paper shows that the nonlinear characteristics of EEG signals extracted based on RQA method can become an objective indicator to distinguish children with ASD and TD, and combined with machine learning methods, the method can provide auxiliary evaluation indicators for clinical diagnosis. At the same time, the difference in the nonlinear characteristics of EEG signals between ASD children and TD children is statistically significant in the parietal-frontal lobe. This study analyzes the clinical characteristics of children with ASD based on the functions of the brain regions, and provides help for future diagnosis and treatment.