Conditional nonlinear optimal perturbations (CNOPs) of a two-dimensional quasigeostrophic model are obtained numerically. The CNOP is the initial perturbation whose nonlinear evolution attains the maximum value of the cost function, which is constructed according to the physical problems of interests with physical constraint conditions. The difference between the CNOP and a linear singular vector is compared. The results demonstrate that CNOPs catch the nonlinear effects of the model on the evolutions of the initial perturbations. These results suggest that CNOPs are applicable to the study of predictability and sensitivity analysis when nonlinearity is of importance.