Sharp optical resonances associated with quasi-bound states in the continuum (Q-BIC) in a single nanostructure have emerged many promising applications, such as lasers, sensors, and non-linear optical devices. Here, we theoretically demonstrate a Q-BIC mode with a Q-factor of >700. A configuration combining a silicon (Si) disk resonator and a metallic substrate supports two higher-order azimuthal eigenmodes which exhibit a large mode overlap and thus results in the high-Q-factor Q-BIC mode. We theoretically demonstrated the application of the Q-BIC mode to refractive index (RI) sensing with a small footprint of ~1.0 um^2 and a sensitivity of 15.4 nm/RIU.