Abstract: For far infrared (FIR) and terahertz (THz) spectrum, the photodetectors conventionally are made from narrow gap semiconductors and quantum well structures. These detectors operate by electron (hole) transition via intra-band (inter-subband) on the basis of quantum well structures. Nowadays using the graphene nanoribbon field effect transistors effective detectors in the range FIR and THz optical spectrum designed and fabricated. The ability to change the bandgap of graphene nanoribbon by altering nanoribbon width has aided multicolor optical detectors to be made. In this paper the operation of a graphene semiconductor nanoribbon phototransistor has been investigated and also some of its characteristics like photonic current, dark current and responsivity has been calculated and plotted. The obtained ratio of the photonic current to dark current for the back gate voltages at 0.5, 1, and 1.5 V reaches to more than one order. The calculated quantum efficiency, responsivity and photonic current of these photodetectors show higher quantities than that of conventional photodetectors.