Electroencephalography (EEG) is an effective assessment tool to identify autism spectrum disorders with low cost, and deep learning has been applied in EEG analysis for extracting meaningful features in recent years. However, as a kind of neural electrophysiological signal, EEG contains different types of temporal and spatial information. Therefore, we propose a lightweight spatio-temporal attention-based convolutional neural network (LSTA-CNN) for ASD diagnosis based on EEG recordings. It utilizes multi-scale temporal and spatial convolution layers to simultaneously learn diverse representations from the time and spatial domain. Meanwhile, we introduce a new spatio-temporal attention mechanism, which can jointly integrate features from the temporal domain and spatial domain, enabling our model to extract EEG features effectively. We performed extensive experiments on our self-collected EEG recordings of 41 autistic children and 32 normal control children. Compared with some representative deep learning models, e.g., Shallow ConvNet, EEGNet, etc., our proposed LSTA-CNN achieves the best classification performance on our self-collected EEG dataset. In addition, our model has significantly fewer numbers of parameters and requires less inference time, which indicates it is lightweight and has great potential in practical applications.