The nonlinear optimization methods are applied to quantify the predictability of a numerical model for El Nino-Southern Oscillation (ENSO). We establish a lower bound of maximum predictability time for the model ENSO events (i. e. ENSO events in the numerical model), an upper bound of maximum prediction error, and a lower bound of maximum allowable initial error, all of which poENSO event and support the previous views on SPB. Additionally, we also explore the differences between the linear evolution of prediction error and its nonlinear counterpart. The results demonstrate the limitation of linear estimation of prediction error. All these above resuits suggest that the nonlinear optimization method is one of the useful tools of quantifying the predictability of the numerical model for ENSO.