A class of solar-forced recharge oscillator model for the El Niño /Southern Oscillation (ENSO) is considered. By transforming the ENSO model equations into the van der Pol-Duffing oscillator with periodic forcing, we obtain the Hopf bifurcation conditions by the harmonic balance method. Numerical simulations also show that the 11-yr solar-cycle forced ENSO system undergoes a transition from the quasi-periodicity route to chaos as the solar-cycle forcing is increased.