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 fitting 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 sensors on the plane, which impairs the flight performance and efficiency of flight controller and actuators. 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 stabilize 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 different parameters of observer and the comparison with several classic methods, such as Kalman filter, 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.