This paper presents a new approach to classify human motions using a Doppler radar for applications in security and surveillance. Traditionally, the Doppler radar is an effective tool for detecting the position and velocity of a moving target, even in adverse weather conditions and from a long range. In this paper, we are interested in using the Doppler radar to recognize the micro-motions exhibited by people. In the proposed approach, a frequency modulated continuous wave radar is applied to scan the target, and the short-time Fourier transform is used to convert the radar signal into spectrogram. Then, the new two-directional, two-dimensional principal component analysis and linear discriminant analysis are performed to obtain the feature vectors. This approach is more computationally efficient than the traditional principal component analysis. Finally, support vector machines are applied to classify feature vectors into different human motions. Evaluated on a radar data set with three types of motions, the proposed approach has a classification rate of 91.9%.