Bi-directional dual-wavelength multi-mode Brillouin lasing based on the unbalanced Mach-Zehnder interferometer (UMZI) hybrid fiber ring cavity is realized experimentally with frequencies of heterodyne spectrum between pump and Stokes lights being 10.49 GHz and 10.54 GHz, respectively. Frequency shift of bi-directional Stokes light′s beat spectrum is measured, and results show that the frequency shift linearly increases with the increase of rotating speed of cavity. The lock-in effect is not observed in the range of measurement, and rotating direction of cavity can be clearly distinguished through relative frequency shift. This provides a novel way for designing Brillouin fiber-optic gyroscope (BFOG). The measured scale factor of gyroscope is 1.0305 kHz/(°·s-1), which fits well with the result of theoretical analysis.