A novel THz antenna structure, made of carbon nanotube arrays is suggested.Using CST MICROWAVE STUDIO (CST MWS), the capabilit ies of carbon nanotube terahertz (THz) antenna arrays have been simulated. The dependence of gain, upon geometrical factors, e.g., nanotube diameter, nanotube length and the inter-tubes distance, is shown. The directivity patterns of antenna arrays and the surface current distribution of an antenna have been shown by simulation. These results could be used in the design ofcarbon nanotube THz antenna arrays.