The sectorial oscillation of acoustically levitated viscous drops is investigated by applying a series of aqueous glycerol solutions (viscosity = 0.9475.65 mPas). It is found that there exists a critical viscosity c for a definite mode of sectorial oscillation, and that mode can be excited only when c. The critical viscosities for the l = 29th mode sectorial oscillation are experimentally determined with a modulation amplitude to the acoustic field reaching = 0.23. It is found that ln c decreases approximately linearly with l. Analysis based on the parametric resonance theory indicates that in order to excite the sectorial oscillation, the equatorial radius of the drop must be perturbed overs a threshold hc, which is proportional to the viscosity and increases with l. Therefore, the sectorial oscillations can hardly be excited to those drops with high viscosity and large oscillation modes. Both the amplitude and resonant modulating frequency width decrease with the enlargement of viscosity. No obvious effect of viscosity is found on the eigenfrequency of sectorial oscillation.