This study investigates the design of a position controller for a tail-sitter micro aerial vehicle (MAV) during the hover stage. Relative small mass and moment of inertia make this kind of aircraft have coupling issues between longitude and lateral, disturbance sensitive and hard to model accurately. Nonlinear dynamic models including uncertainties are built first, the systems are then divided into the combination of an uncertainty-free nominal system and a nonlinear unmatched uncertainty. The cascaded nonlinear dynamic inversion controller is used to control the uncertainty-free system to guarantee the good command tracking ability. Explicit express of the desired dynamics makes this architecture more appropriate to integrate with the L1 adaptive controller. The L1 adaptive controller is then used to compensate for the nonlinear unmatched uncertainties to improve robustness and transient performance of the system. In order to reduce the complexity of operation and be easy to realize in engineering, the proportional adaptation law is used as the architecture of the L1 adaptive controller because of its relative low computation consumption. Simulation results verify the good command tracking ability in position and altitude of the controller.