Compared with face recognition in the environment of visible light, thermal infrared face recognition has the advantages of being independent of light, working around the clock, and capable of detecting hidden targets easily. In this paper, we propose a thermal infrared face recognition method based on the two-directional two-dimensional PCA (2D2DPCA) and random forest classifier. We compared this with two deep learning networks: Alexnet, Three-dimensional Convolutional Neural Networks (3DCNN), and applied these with two databases: the Terravic Facial IR database (with different facial angles) and the NVIE database (with various emotional expressions). Among these methods, the accuracy of face recognition with the 2D2DPCA method achieves the best recognition effect, it reached 99.92% and 99.97% in both databases, respectively. We statistically verified that our method could not only accurately and robustly recognize thermal infrared faces with large variations in angle and expression, but also greatly reduce computational complexity and data dimension, improving the speed of face recognition. With the two sample sets tested, our work has demonstrated that 2D2DPCA has excellent potential for facial image compression and may broaden thermal face recognition applications.