Graphene has been attracting strong scientific and technological interest for its promising application in the development of biological and chemical sensors. The advantages of high carrier mobility, doping sensitivity and feasibility for device fabrication has made graphene an outstanding candidate material for the development of next generation biomedical sensors. Recently, a variable capacitor (varactor) based on graphene quantum capacitance effect has been studied for the capacitive sensing of target analytes, with the ultimate goal of wireless biomedical sensing. In this dissertation, the graphene varactors were investigated as a sensor platform to carry different surface functionalization for various molecules that are related to early disease diagnostics, demonstrating the potential in the research of passive wireless sensing devices. In Chapter 1, the background of graphene is introduced, including the structure, the history, the properties, and its application in the electronic device fabrication studies. The progress of graphene-based device in the field of semiconductor research is summarized with advantages and disadvantages, which leads to the motivation of this dissertation. In Chapter 2, the graphene varactor device is reviewed with the operation basis, the fabrication process, the device characteristics and the capability to carry various surface functionalization as an advanced sensing platform. In Chapter 3, a glucose sensor based on graphene varactor is developed with device characterization. The device features capacitive signal of glucose in the sensing environment with high ionic strength. In a parallel comparison of a wired measurement, the passive wireless sensing of volatile organic compounds (VOCs) using graphene varactors is demonstrated in Chapter 4. The device performance in the resonant frequency shift was analyzed in a semi-empirical model, showing the reproducible and selective response upon the exposure to different VOC conditions. Finally, the work is summarized with future developments and improvements towards optimized wireless sensing based on graphene varactors in Chapter 5. A novel sensor array with multi-VOC sensing capability is proposed for the application in real time breath monitoring.