During slow level flight of a pigeon, a caudal muscle involved in tail movement, the levator caudae pars vertebralis, is activated at a particular phase with the pectoralis wing muscle. Inspired by mechanisms for the control of stability in flying animals, especially the role of the tail in avian flight, we investigated how periodic tail motion linked to motion of the wings affects the longitudinal stability of ornithopter flight. This was achieved by using an integrative ornithopter flight simulator that included aeroelastic behaviour of the flexible wings and tail. Trim flight trajectories of the simulated ornithopter model were calculated by time integration of the nonlinear equations of a flexible multi-body dynamics coupled with a semi-empirical flapping-wing and tail aerodynamic models. The unique trim flight characteristics of ornithopter, Limit-Cycle Oscillation, were found under the sets of wingbeat frequency and tail elevation angle, and the appropriate phase angle of tail motion was determined by parameter studies minimizing the amplitude of the oscillations. The numerical simulation results show that tail actuation synchronized with wing motion suppresses the oscillation of body pitch angle over a wide range of wingbeat frequencies.