We find that the ordinary universality does not hold for a frustrated spin-1 Ising model with nearest-neighbor bilinear interaction J1 and next-nearest-neighbor bilinear interaction J2 on the square lattice. We estimated critical indices ν, η, and ys by applying the Monte Carlo renormalization-group method to the model. The critical index ν varies with J1/J2 in a region where the ground state is of the super-antiferromagnetic configuration. Although the behavior of ν is analogous to that of the spin-1/2 Ising model as a function of J1/J2, the value of ν appears to be smaller than that of the corresponding spin-1/2 Ising model. The value of η agrees with the value predicted by the Onsager universality class. The crossover exponent ys agrees with the value estimated for the spin-1/2 Ising model.