In a ring laser gyroscope, due to the rotation and the Sagnac effect, a phase difference between the two counter-propagating beams is generated. In this device, the higher phase difference between these two beams causes the better the interference pattern detection, and thus the sensitivity is increased. In this paper, the effect of inserting a dielectric-graphene photonic crystal inside a ring laser gyroscope on the interference pattern and the sensitivity of the device are studied and simulated using ABCD propagation matrix method. Results show that dielectric-graphene photonic crystal has a high transmission and therefore high efficiency in the wavelength of ring laser gyroscope. So it is a suitable choice to use in the ring laser gyroscope. Also, a comparison between ring laser gyroscope with and without dielectric-graphene photonic crystal shows that when the dielectric-graphene photonic crystal is in the system it is possible to build gyroscope with smaller lengths and high sensitivity.