In this paper, a magnetic sensor based on graphene nanoribbon is proposed. The idea of implementation of the sensor is based on the change of propagation constant, and as a result, the refractive index of the graphene nanoribbon over the dielectric substrate. In this sensor, the under measurement magnetic field has perpendicular component to the graphene layer. Therefore, the response to the measured magnetic field is due to the graphene magnetic response, which is in turn due to the resonances originated from cyclotron effect and inter Landau levels transitions. Magnetic field dependent response of graphene can be modeled using the graphene surface conductivity. Based on the model, the performance of the structure is simulated. It is possible to electrically calibrate the structure regarding to the chemical potential dependency of graphene surface conductivity which can be controlled via an external bias voltage. The attained results can be utilized in design of various magnetic sensors for detection and measurement of magnetic fields in different systems.