This paper investigates the trajectory tracking problem for quadrotors with finite-time convergence via homogeneous feedback approach. Based on the inherent underactuated cascaded properties of a quadrotor, the tracking control is decomposed into the outer position tracking control loop and the inner attitude tracking control loop. And the orientation of the four thrust inputs for the position loop is determined by the attitude loop. Therefore, an inner geometric tracking controller based on exponential coordinates for the attitude loop is first proposed, which avoids kinematic singularity and redundancy. Then, a homogeneous feedback plus dynamics compensation scheme is utilized to construct the thrust magnitude control input for the position dynamics, which also provides a reference rotation matrix for the attitude tracking loop. The almost global finite time stability of the whole tracking control system is clearly proved. Numerical results are also presented to demonstrate the effectiveness of this finite-time control strategy.