We examine and analyze vibrational resonance (VR) in a dual-frequency-driven gyroscope subject to a parametric excitation and an additive periodic forces. The method of direct separation of the fast and slow motions is used to derive the response amplitude analytically from the equation for slow oscillations of the system, in terms of the parameters of the high-frequency signal and the parametric excitation. Numerical simulations are carried out to validate the theoretical results. It is further shown that, when the parametric excitation and additive periodic force consist of low and high frequencies, respectively, a much higher response amplitude can occur. It is about three times larger than the response obtained when the forcing actions are reversed and is attributable to the optimization of low-frequency parametric excitation by the high-frequency additive signal.