Flapping-wing micro air vehicles (FWMAVs) inspired by the nature are interesting flight platforms due to their efficiency, concealment and agility. However, most studies have been conducted in indoor environments where external disturbance is excluded because these FWMAVs are susceptible to disturbance due to their complex dynamics and small size. In order for these bio-inspired robots to perform various tasks outside, a capability to react robustly to external disturbance is essential. In this letter, we propose an algorithm that allows a FWMAV to fly well even under external disturbance. First, we derive the attitude dynamics of the FWMAV based on flight data. Then, we design a robust attitude controller using DOBC based on the dynamics. Also, we add a flight mode selector to recognize disturbance autonomously and switch to the robust control mode. Finally, we experiment outdoor flight of the FWMAV with wind disturbance. The FWMAV recognizes the existence of disturbance autonomously, and produces additional control inputs to compensate the disturbance. The proposed algorithm is validated with experiments.