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In this paper, an efficient wave concept iterative process algorithm is proposed to analyze a dynamically controllable grounded coplanar waveguide attenuator based on graphene at terahertz frequencies. The proposed modeling technique of graphene is based on waves concept, that is based on redefining the boundary conditions (surface current and electric field) in terms of incident and reflected waves. The developed algorithm integrates both the interband and intraband conductivities without involving volumetric discretization. Therefore, it consumes less simulation time and computational resources. Numerical studies are conducted to validate the accuracy, speed, and usefulness of the proposed technique. Simulation results demonstrate that the interband term of the graphene conductivity has a significant effect and cannot be neglected in the simulation. The performance of the attenuator can be improved by controlling the chemical potential of graphene, which can achieve an attenuation range from 0.29 to 13.2 dB. [ABSTRACT FROM AUTHOR]