In this work, a CNT based TFET label free biosensor is investigated. A nanogap is introduced under the gate at the source side where the biomolecules are fed. The drain current of the TFET depends on the gate dielectric material. Thereby, sensing of the biomolecules is achieved by dielectric modulation. The sensitivity of the device is studied in terms of the ON-current and also in terms of the threshold voltage. The effect of the cavity length and dielectric constant of the gate insulator on the sensor sensitivity is investigated. Also, the CNT chirality index is adjusted for better sensitivity. The device performance for biosensing applications is analysed for different biomolecules with different dielectric constants. Moreover, the sensitivity of the sensor for both neutral and charged biomolecules is examined. A quantum 2D simulator, which is based on self-consistent solution of non-equilibrium Green's function and Poisson's equation, is utilized to study the device performance. A higher device sensitivity is achieved by using low-k gate oxides and CNTs with higher chirality index. In addition, sensitivity and selectivity increases for higher charge density biomolecules. The results, provided in this work, demonstrate the ability of CNT-TFETs to function as a free-label biosensor.