In order to optimize the performance of the coupled resonator optical waveguide (CROW) gyroscope, a well-designed structure by optimizing the ring number and the transmission coefficient of the coupler is used as the core component of the planar waveguide optical gyroscope. The structure with double coupled ring resonator may possess large effective group refractive index to enhance angular sensing sensitivity was proposed. The concept of the Sagnac effect in this new double coupled ring resonator structure with a large effective group refractive index is investigated, it’s found that the rotation-induced phase shift is proportional to the effective group refractive index. On the basis of this effect, we calculate the general relation expression of theoretical rotation sensitivity and the effective group refractive index for this two-ring bidirectional CROW gyroscope by numerically simulation. Based on the relation, the phase shift characteristics of double coupled ring resonator and single ring resonator was analyzed. And the changing characteristics of the transmission coefficient of the couplers and the effective group refractive index was discussed based on the double cascaded ring resonator coupling mode theory. In the case of R1=R2=100 μm and ring transmission loss coefficient t1=t2=0.95, the generating condition of the largest effective group refractive index was obtained, according to the different effects of the couplers between rings and waveguide on the effective group refractive index. By using the parameters of R=100 μm and t=0.95, the sensitivity of a single ring resonator gyroscope is (104-105) °/h, and the sensitivity of double coupled ring resonator gyroscope can reach to 10 °/h. In summary, we show that the theoretical sensitivity of the double coupled ring gyroscope and single ring gyroscope are comparable when both have the same parameters. Using numerical and analytical methods, we demonstrated that coupling multiple resonators together can enhance rotation sensitivity. This research is important for applications of coupled ring resonator in optical angular velocity detection, and a promising regime to realize highly compact optical gyroscope.