Based on the first-order shallow water equation with approximate geostrophic effect, the interaction between nonlinear Kelvin and Rossby waves in the low-latitude air-sea coupling system is analyzed by using multi-scale and perturbation approximation methods. The results are listed below. (1) When there is no wind stress, the amplitude of the coupling wave is small, and the amplitudes of Kelvin and Rossby waves 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, Kelvin wave oscillates quasi periodically, Rossby wave oscillates aperiodically, and this superposition effect of quasi-periodic and aperiodic oscillations reflects the quasi-periodic oscillation characteristics of ENSO (El Nio-Southern Oscillation) with weak periodicity. (3) In the ENSO movement, Kelvin and Rossby waves always exist. Due to the nonlinear interaction, they show different states at different stages, namely dormancy (brewing)-growth-attenuation-dormancy (brewing) as a whole.