Driver drowsiness is a major cause of road accidents. In this study, a novel approach that detects human drowsiness is proposed and investigated. First, driver face and facial landmarks are detected to extract facial region from each frame in a video. Then, a residual-based deep 3D convolution neural network (CNN) that learned from an irrelevant dataset is constructed to classify driver facial image sequences with a certain number of frames for obtaining its drowsiness output probability value. After that, a certain number of output probability values is concatenated to obtain the state probability vector of a video. Finally, a recurrent neural network is adopted to classify constructed probability vector and obtain the recognition result of driver drowsiness. The proposed method is tested and investigated using a public drowsy driver dataset. Experimental results demonstrate that similar to 2D CNN, 3D CNN can learn spatiotemporal features from irrelevant dataset to improve its performance obviously in driver drowsiness classification. Furthermore, the proposed method performs stably and robustly, and it can achieve an average accuracy of 88.6%.