This study aims to explore the possibility of using a multilayer artificial neural network for the classification between children with autism spectrum disorder (ASD) and typically developing (TD) children based on short-time spontaneous hemodynamic fluctuations. Spontaneous hemodynamic fluctuations were collected by a functional near-infrared spectroscopy setup from bilateral inferior frontal gyrus and temporal cortex in 25 children with ASD and 22 TD children. To perform feature extraction and classification, a multilayer neural network called CGRNN was used which combined a convolution neural network (CNN) and a gate recurrent unit (GRU), since CGRNN has a strong ability in finding characteristic features and acquiring intrinsic relationship in time series. For the training and predicting, short-time (7 s) time-series raw functional near-infrared spectroscopy (fNIRS) signals were used as the input of the network. To avoid the over-fitting problem and effectively extract useful differentiation features from a sample with a very limited size (e.g., 25 ASDs and 22 TDs), a sliding window approach was utilized in which the initially recorded long-time (e.g., 480 s) time-series was divided into many partially overlapped short-time (7 s) sequences. By using this combined deep-learning network, a high accurate classification between ASD and TD could be achieved even with a single optical channel, e.g., 92.2% accuracy, 85.0% sensitivity, and 99.4% specificity. This result implies that the multilayer neural network CGRNN can identify characteristic features associated with ASD even in a short-time spontaneous hemodynamic fluctuation from a single optical channel, and second, the CGRNN can provide highly accurate prediction in ASD.