First arrival time picking is one of the critical processing steps of acoustic emission (AE)/microseismic (MS) monitoring for studying rock fracture processes. Because of massive monitoring data, the automatic arrival time picking technique is particularly desired. Inspired by recent successful applications of machine learning (ML) in earthquake phase identification, we propose a deep learning (DL)-based P-wave first arrival time picking method named AE Network (AEnet) for laboratory AE monitoring data. Our approach consists of two steps: classification and picking. The convolutional neural network (CNN) is used to classify each sample point of acoustic waveforms into either noise or signal. Different from prior DL-based phase picking studies using raw waveforms, we combine the waveform and high-order statistics as the input to enrich the input data features and accelerate the CNN model learning process. Our approach is examined using the laboratory AE monitoring data and the performance of each component of AEnet is also analyzed. The results show that the CNN model can classify the sample points accurately for the picking procedure. With this classification result, we pick the first arrival time of each trace using the curve fitting method and an unsupervised clustering algorithm. To evaluate the performance of AEnet, we apply Akaike Information Criterion-Short Term Averaging/Long Term Averaging Method (AIC-STA/LTA), one of the most popular and traditional picking methods, on the same waveforms and use the manual picks as the reference. Error analysis results show that AEnet outperforms AIC-STA/LTA.