Via a simple mathematical model，the flight mechanism was studied，known as the dipteran flight oscillator. Aiming at dipteran flight oscillator，the stability and complicated dynamic behaviors were investigated. Codimension-two bifurcation of nonlinear phenomena was discovered near trival solution. Nonlinear viscous damping was introduced. Furthermore，applying the rescaling of the state and time variables，the universal unfolding and the relationship between its parameters and the parameters of the original nonlinear dynamical system were obtained. The investigation was made on the effects of nonlinear viscous damping on the codimension dynamical bifurcation. Based on this equivalence between the universal unfolding and the damped system，the bifurcation diagram and the corresponding co-dimension two behavior near the trivial equilibrium were obtained and displayed for the damped dipteran flight oscillator as the perturbation parameters vary.