In this paper, the double-walled carbon nanotube composite material (DWCNTscomposite) and bundle of DWCNT-composite material (CB-DWCNTs) for antenna applications at terahertz frequency range are presented and investigated. The mathematical modeling and analysis of DWCNTs-composite material is presented for the purpose of modelling and simulation approach. The bundle of DWCNTs-composite material is constructed and designed, based on this modeling approach. The DWCNT-composite material consists of double-walled carbon nanotube coated by a thin jacket of another different material. The dependency of the electrical conductivity of B-DWCNTs-composite on different parameters is presented and investigated. The performance evaluation of B-DWCNTscomposite and CB-DWCNTs materials are presented based on their electromagnetic properties. For this purpose, the dipole antennas of these composite materials are designed and implemented using CST (MWS), where the cross sections of B-DWCNTs-composite and CB-DWCNT materials are circular geometry. Furthermore, comparative studies are performed to show the dependency of size and frequency of the DWCNT-composite material. The results obtained from the DWCNTs-composite and CB-DWCNTs dipole antennas are presented based on S 11 parameters, resonant frequency, gain, bandwidth, and efficiency.