Research and practical application have been developed utilizing terahertz gap between microwave and infrared light. Among that, Terahertz device utilizing field-effect transistors (FETs) such as III-V high-electron mobility transistors or Si-based metal oxide semiconductor transistors has been recently researched. Terahertz detection in FETs is mediated by the excitation of plasma waves within the channel of transistor. In this work, terahertz detection based on plasma wave response in graphene field-effect transistor are demonstrated and analyzed. In the first chapter, relative theory and research background is introduced. In the second chapter, the fabrication of graphene-field effect transistor and its optimization is discussed. In the third chapter, enhanced transconductance, which is essential for a high responsivity FET sensor, in a graphene-field effect transistor by adopting additional gate is studied. In the fourth chapter, short channel graphene field-effect transistor for enhanced plasma wave response is fabricated, and their performance is measured and analyzed.