In this work, a graphene hybrid plasmonic waveguide has been studied employing the finite element method. The graphene layers have been exploited here as optical absorber layers to extinguish the undesired plasmon modes in our system. Also, the silicon nanowires in our design, have been utilized to form a hybrid plasmon waveguide in order to achieve a high figure of merit of the desired plasmon mode. The multiwavelength operability and performance variation with respect to the alteration of waveguide cross-section are investigated here to demonstrate its high promise in broadband single mode operation, design of mode division multiplexing nanoplasmonic systems, and highly compact photonic integration. Furthermore, the effect of graphene’s optical anisotropy on waveguiding is explored here to predict the device performance more realistically.