This paper aims to model and analyze planar antennas for high frequencies using an iterative wave design procedure (WCIP). The formulation adopted in the method allowed determining a basic equation for the interaction of linearly combined electromagnetic fields with the incident and reflected waves in various dielectric media over a discontinuity. In this paper, we design a broadband terahertz patch antenna using graphene. We propose to design a new numerical tool to model the implementation of graphene to achieve an efficient and flexible antenna. The design methodology started with the design of a compact conventional microstrip antenna for 118.87 GHz, and the antenna was then miniaturized using rectangular slots. Based on the simulation results, the suggested structure antenna with a slot can offer great characteristics in terms of broadband performance and frequency reconfiguration using various voltages on the graphene. The antenna provides frequency bands f r1 = 118.7 GHz, f r2 = 120 GHz, f r3 = 123.36 GHz, f r4 = 128.27 GHz, f r5 = 131 GHz, and f r6 = 132.8 GHz with bandwidths ∆f r1 = 9.5 GHz, ∆f r2 = 3.66 GHz, ∆f r3 = 4 GHz, ∆f r4 = 3.23 GHz, ∆f r5 = 3.401 GHz, ∆f r6 = 3.01 GHz and uniform radiation patterns, the value of VSWR between 1 and 2 for different chemical potential values respectively µ c = 0.1 eV, µ c = 0.2 eV, µ c = 0.3 eV, µ c = 0.4 eV, µ c = 0.5 eV, µ c = 0.6 eV using polyimide with a dielectric constant of 3.5 and a loss tangent of 0.008. In addition, we studied the effect of different substrate materials (Arlon and Duroid 5880). The simulation is performed using a new WCIP equation, and the validation is performed by comparison with the finite integration method in technique (FIT). A comparison of the computation time is presented in this paper.