This paper researches a new tail-sitter UAV. Considering its configuration characteristics, a dual-Euler method was applied to solve the singularity problem of the pitch angle when the tail-sitter UAV tilts the fuselage. Aiming it is easily interfered in flight process, L1 adaptive control method was used to design control law to ensure that the UAV had a good controllability and stability in mode transition. The effective of model and controller law were verified by simulation experiment. The results of simulation experiment show that the controller can overcome interference from its parameter perturbation and other uncertainty. This provides a new scheme for the design of flight control law and engineering realization of tail-sitter UAV.