This paper presents the design and simulation of a Modified State Observer (MSO) based adaptive control law, developed by Balakrishnan, for a Micro Aerial Vehicle (MAY). The MSO allows higher adaptive gains than other adaptive control laws. The simulation is carried out using the aerodynamic derivatives of the Black Kite 300 mm wing span MAV developed by CSIR-NAL Bangalore. The controller is tested in simulation for its ability to adapt to modeling errors for the highly responsive MAV. At present, the study is limited to the longitudinal dynamics of the vehicle. Simulation results are presented that show the controller's ability to respond to altitude and airspeed commands with elevator and engine failures in the presence of parameter uncertainties. The MSO adaptation along with the nonlinear dynamic inversion controller developed using the mathematical model of the MAV, enables the pilot to control the vehicle with a lower workload.