The periodically time-varying forces make the equilibrium state of Beihawk, an X-shaped flapping-wing aircraft, to be a periodic limit cycle oscillation. However, traditional controllers based on averaging theory fail to suppress this oscillation and the derived stability result may be inaccurate. In this study, a period-based method is proposed to design the oscillation suppression controller, locate the corresponding cycle and analyze its stability. A periodically time-varying wing-tail interaction model is built and Discrete Fourier Transform is applied to adapt the model for controller design. The harmonics less than quintuple flapping frequency account for more than 96 percent of the total harmonics and are reserved to present a concise model. Based on this model, Active Disturbance Rejection Controller (ADRC) is designed and its Extended State Observer can observe the disturbance to suppress the oscillation.Poincaré map is introduced to convert the stability analysis of the cycle to a fixed point. A multiple shooting method is adopted to locate several points on the cycle and