Glucose, sucrose and fructose are typical organic compounds having carbon-hydrogen-oxygen atoms. Their sensing is important in many bio-medical applications. In this paper we present a 2D material-based fiber optic surface plasmon resonance sensor for refractive index sensing of some typical organic compounds. 2D material graphene in combination with active metal gold is used in the sensing region. Fiber core is covered with gold and graphene layer. The sensor is simulated using COMSOL Multiphysics simulation software. To measure the sensing performance of sensor we see the effect of two physical parameters of the sensor, thickness of the Au-metal and graphene layer on the sensing performance. The use of graphene layer enhances the sensitivity of SPR sensor. The angular interrogation method of SPR excitation is used for sensor simulation in COMSOL Multiphysics.