Our wavelet analysis of Archiving, Validation and Interpretation of Satellite Oceanographic Data (AVISO) sea surface height anomaly reveals an oscillation with a period of 30 days, which exists only inside the western boundary current region. The mechanism may be an instability of cross-equatorial current. The research tool is a simple equivalent shallow water model in the presence of background cross-equatorial current. By expanding the perturbation equation with Weber function and keeping the first four modes, the dispersion relation in the presence of cross-equatorial current is obtained. Our instability analysis demonstrates the existence of unstable modes in this boundary current region. The most unstable shortwave has a period of approximate 30 days, which is in accordance with the AVISO observations.