In simulation of long-span bridge and airfoil flutter, a large-amplitude motion-induced force model is required. However, existing time-domain motion-induced force models cannot simulate memory effects and amplitude dependency simultaneously. This paper proposes a new time-domain non-linear motion-induced force model, which employs a set of nonlinear differential equations and augmented aerodynamic degrees of freedoms to simulate memory effects and amplitude dependency. Motion-induced forces under different deck motion amplitudes, different reduced wind velocities and non-sinusoidal motions can be simulated using a single set of model parameters. A fitting algorithm for the new model is also proposed and the model parameters of a bridge deck are fitted using results obtained by CFD simulations. Numerical example shows that the new model can reproduce variation of aerodynamic damping characteristics with reduced wind velocity and amplitude. A model fitted using single-frequency forced vibration tests can reproduce forces generated by multi-frequency vibrations.