Radio frequency fingerprint (RF fingerprint) extraction is an important technology employed to identify the unique radio transmitter at the physical level regardless of specific information carried. RF fingerprint contains rich nonlinear characteristics and reflects the differences of internal components in radio transmitters. RF fingerprint extraction and identification has been extensively adopted to enhance the security of radio frequency communication in both military and civilian use. In this paper, we propose a novel RF fingerprint based on singular values and singular vectors of time-frequency spectrum with extremely little demand of priori information and introduce a better suited classifier known as Gaussian Mixture Model compared to support vector machine. A communication system that can capture the signals from three same type radios is designed to evaluate the method. The proposed method can achieve higher classification accuracy than that of other two RF fingerprint extraction methods. And it shows well qualified robustness under different SNR. The experiment results demonstrate the practicality of our proposal.