This paper establishes and analyzes a high-fidelity nonlinear time-periodic dynamic model and the corresponding state observer for flapping vibration suppression of a novel tailless Flapping Wing Micro Air Vehicle (FWMAV),named NPU-Tinybird.Firstly,a complete modeling of NPU-Tinybird is determined,including the aerodynamic model based on the quasi-steady method,the kinematic and dynamic model about the mechanism of flapping and attitude control,combined with the single rigid body dynamic model.Based on this,a linearized longitudinal pitch dynamic cycle-averaged model is obtained and analyzed through the methods of neural network fit-ting and system identification,preparing for the design of flapping vibration suppression observer.Flapping vibration is an inherent property of the tailless FWMAV,which arises from the influence of time-periodic aerodynamic forces and moments.It can be captured by attitude and position sen-sors on the plane,which impairs the flight performance and efficiency of flight controller and actu-ators.To deal with this problem,a novel state observer for flapping vibration suppression is designed.A robust optimal controller based on the linear quadratic theory is also designed to sta-bilize the closed-loop system.Simulation results are given to verify the performance of the observer,including the closed loop responses combined with robust optimal controller,the comparison of dif-ferent parameters of observer and the comparison with several classic methods,such as Kalman fil-ter,H-infinity filter and low-pass filter,which prove that the novel observer owns a fairly good suppression effect on flapping vibration and benefits for the improvement of flight performance and control efficiency.