A weakly nonlinear model is proposed for the Kelvin-Helmholtz instability by expanding the perturbation velocity potential to third order. It is found that there is an important resonance in the process of mode coupling. This resonance makes the coupling processes very complex and interesting. Single-mode perturbation enters nonlinear stage quickly and produces lots of harmonics. The resonance reinforces the action of nonlinear process. The second and third harmonic generation efficiency of a single-mode disturbance is computed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. Our simulations support the weakly nonlinear results from our analytic model. The nonlinear threshold phenomenon is also analyzed.