The critical current of the self-oscillation of spin torque oscillator (STO) consisting of a perpendicularly magnetized free layer and an in-plane magnetized pinned layer was studied by solving the Landau-Lifshitz-Gilbert (LLG) equation. We found that the critical current diverged at certain field directions, indicating that the self-oscillation does not occur at these directions. It was also found that the sign of the critical current changed depending on the applied field direction.