A double closed-loop resonant micro optic gyro (RMOG) employing a hybrid digital phase modulation technique is demonstrated, showing encouraging progress. In this hybrid modulation scheme, the width of one stair of the stair-like digital serrodyne wave is optimized according to the rise time of the digital-to-analogue converter to obtain the maximum sideband suppression. Based on the optimum parameters of the hybrid modulation scheme, a typical bias stability of 0.05/s in 1 hr is demonstrated in an RMOG with a silica waveguide ring resonator having a ring length of 7.9 cm. This is the best long-term performance which has ever been reported in an RMOG to our knowledge.