Based on the first order shallow water equation of approximate geostrophic effect, the interaction of nonlinear Kelvin waves and Rossby waves in the low latitude air sea coupling system is analyzed by using multi-scale and perturbation approximation methods. The results show that: (1) when there is no wind stress, the amplitude of the coupling wave is small, and the amplitudes of Kelvin wave and Rossby wave are quasi periodic. This quasi periodic change is the result of the kink effect and the nonlinear effect of the two types of waves; (2) When there is wind stress, the amplitude of the coupling wave will increase after the exponential spiral oscillation, Kelvin wave will oscillate quasi periodically, Rossby wave will oscillate aperiodically, and this superposition effect of quasi periodic and aperiodic oscillations reflects the quasi periodic oscillation characteristics of ENSO with weak periodicity; (3) In the ENSO movement, Kelvin wave and Rossby wave always exist. Due to the nonlinear interaction, they show different states at different stages, as a whole: dormancy (brewing) → growth → attenuation → dormancy (brewing).