By using the local field enhancement of the optical Tamm state (OTS) at the interface of metal-distributed Bragg reflector(DBR) and the electronic control characteristics of graphene, we propose a graphene based light modulator based on OTS. The proposed optical modulator is simulated by finite element method and finite difference time domain method. The results show that when the incident wavelength is 850.7 nm, OTS can be engendered at the metal-DBR interface and the reflectivity of incident light is relatively low. When the driving voltage is greater than 7.5 V, the intrinsic wavelength of OTS drifts and the reflectivity of incident light increases, so that intensity modulation can be achieved. The maximum modulation depth of the optical modulator can be up to 0.96 and the extinction ratio is 14.45 dB. Without considering the effect of RC time constant on the modulation rate, the modulation rate is above 600 GHz. The proposed graphene modulator can be modulated with different modulation depths in a certain wavelength range. It has a good application prospect in the optical communication system and the optical information processing system in the future.