We investigate a graphene and vanadium dioxide (VO2)-based planar antenna with higher-order transverse magnetic (TM) mode for terahertz (THz) applications. The planar antenna is made up of graphene and VO2 materials. Adding graphene and VO2 makes antenna is even more innovative because it conducts electricity really well and makes the antenna more robust and better in performance. The proposed antenna is excited by proximity coupling with Y shape structure. The planar configuration offers single-band operation with resonant frequency 2.98 THz. The proposed antenna provides a maximum directivity of 9.1 dBi with better co and cross polarization. Further, it supports TM modes with a number of higher modes based on the placement of its radiating elements. These modes are characterized as TM42, TM64, and TM76, and so on. In addition, parametric analysis is essential to investigate how the changes in the parameters affect the performance of the antenna. The examinations of these dependencies have been carried out. The proposed antenna may play a vital role in the THz applications such as biomedical and medical imaging applications which often require precise and high-resolution imaging capabilities that THz frequencies provide.