Autism spectrum disorder is a kind of mental disease which involves the disorders of the perception, emotion, memory, language, intelligence, thinking, action, etc. The aim of this paper is to investigate the brain activity characteristics of the children with autism during complex environments by analyzing electroencephalogram (EEG) signals from the neuroergonomics perspective. The virtual driving environment as a complex multi-task source is used to organically connect brain systems with human motion control. The 14-channel EEG signals are obtained including the EEG baseline signals on a resting state (about 3 min) and the EEG activity signals during driving (about 5 min). The method of the shift average sample entropy is proposed to deal with EEG signals in the resting and the virtual driving environments. Considering the highly complex hyper-dimensional characteristics of EEG signals, the different embedding dimensions (such as 2 and 6 dimensions) are analyzed in the sample entropy estimation. The results show that the average sample entropy values of autism spectrum disorder (ASD) subjects are lower than those of healthy subjects during resting and driving, respectively, especially in the prefrontal lobe, temporal lobe, parietal lobe and occipital lobe during resting and in temporal lobe and occipital lobe during driving. It indicates that ASD children lack the ability to adapt easily their behaviors. Meanwhile, like healthy subjects, the average sample entropy values of ASD subjects during driving are higher than those during resting as a whole. Moreover, the EEG activity signals of ASD are obviously higher than the EEG baseline signals in prefrontal lobe, frontal lobe, frontal central lobe and temporal lobe regions in 95% significant level. And for healthy subjects, the activity signals are significantly higher than the baseline signals only in parietal lobe region. Furthermore, the brain activities of ASD subjects during driving come closer to those of healthy subjects during resting. It suggests that the virtual driving environment may be helpful for the treatment of ASD individuals. In addition, the ASD and healthy subjects have a certain right hemisphere dominance in the whole region except in the parietal lobe region. In the parietal lobe region, they have some left hemisphere dominance, especially during driving. And for ASD subjects, there is the significant right hemisphere dominance in the temporal lobe in 95% confidence level no matter whether in the resting state or in the driving state. The results show that it is suitable for the shift average sample entropy analysis to study the brain activities of ASD individuals. This study will provide a new research method for the further research on the mechanism of autism and its diagnosis, evaluation and intervention.