The tilt rotor unmanned aerial vehicle (TRUAV) has attracted considerable attention in recent years, and its control design, particularly during the transition procedure, is still a challenge. Aiming at this difficulty and by introducing virtual control inputs, a nonlinear model of the TRUAV as an equivalent linear parameter varying (LPV) system for controller design of these virtual values is considered in this study. With this idea, one of the main contributions of this paper is that the stability of TRUAV during the transition procedure could be ensured asymptotically in theory. An observer-based LPV control with fault-tolerant ability is synthesized considering the unmeasurable varying parameters of this LPV controlled plant and the underlying sensor faults. The second main contribution is to analyze the closed-loop stability with unmeasurable features and bias sensor faults using parameter-dependent Lyapunov matrices. The performances of proposed control method for TRUAV under sensor faults are illustrated with numerical results.