This paper mainly addresses the problem of current sensorless finite time control for buck-boost converter with unknown constant power load. The negative impedance of constant power loads cause low frequency oscillation, which adversely affect the stability of the system. First, to reconstruct unavailable inductor current and unknown power load, a reduced-order generalized parameter estimation based observer with finite time convergence is developed on the basis of dynamic regressor extension and mixing technique, which is able to reformulate state observation as parameter estimation. Secondly, based on a feedback linearization method, this nonlinear system is transformed into a linear system and a fast terminal sliding mode controller is designed to stabilize the system. Subsequently, a current sensorless finite time controller for this system is proposed by combining a fast terminal sliding mode controller with a generalized parameter estimation based observer. Based on the finite time stability result of the cascaded system, the finite time stability of closed-loop system is proved. Finally, the effectiveness of the proposed current sensorless finite time control is verified by simulation and experiment results.