The early diagnosis of children with autism spectrum disorders (ASD) is essential. Electroencephalography (EEG) is one of most commonly used neuroimaging techniques as the most accessible and informative method. In this study, approximate entropy (ApEn), sample entropy (SaEn), permutation entropy (PeEn) and wavelet entropy (WaEn) were extracted from EEGs of ASD child and a control group, and Student's t-test was used to analyze between-group differences. Support vector machine (SVM) algorithm was utilized to build classification models for each entropy measure derived from different regions. Permutation test was applied in search for optimize subset of features, with which the SVM model achieved best performance. The results showed that the complexity of EEGs in children with autism was lower than that of the normal control group. Among all four entropies, WaEn got a better classification performance than others. Classification results vary in different regions, and the frontal lobe showed the best performance. After feature selection, six features were filtered out and the accuracy rate was increased to 84.55%, which can be convincing for assisting early diagnosis of autism.