A novel method for power system first-swing transient stability fast detection is proposed in this paper. Based on the convexity and concavity of phase-plane trajectory, motion characteristic of phase-plane trajectory is further studied, and a novel criterion for first-swing transient stability detection is proposed. The stability can be detected before the trajectory reaches its Farthest Point (FEP), and instability can be detected before the trajectory passes through the Dynamic Saddle Point (DSP). The efficiency and validity is verified by simulation results on OMIB system and IEEE 39-bus 10-unit system.