An analytical device model for a graphene nanoribbon phototransistor (GNR-PT) is presented. GNR-PT is based on an array of graphene nanoribbons with the side source and drain contacts, which is sandwiched between the highly conducting substrate and the top gate. Using the developed model, we derive the explicit analytical relationships for the source-drain current as a function of the intensity and frequency of the incident radiation and find the detector responsivity. It is shown that GNR-PTs can be rather effective photodetectors in infrared and terahertz ranges of spectrum.Photodetectors for far infrared (FIR) and terahertz (THz) ranges of spectrum are conventionally made of narrow-gap semiconductors and quantum-well structures. In the former case, interband transitions due to the absorption of photons are used. The operation of the detectors based on quantum-well structures is associated with the electron or hole intraband (intersubband) transitions [1, 2]. Some time ago, quantumdot and quantum-wire detectors were proposed [3,4]. The transition from quantum well structures with twodimensional electron (hole) spectrum to low-dimensional structures such as quantum-wire and quantum-dot structures might lead to a significant improvement of the FIR and THz detectors (see, for instance, ref.[5] and the references therein). The utilization of graphene, i.e., a monolayer of carbon atoms forming a dense honeycomb two-dimensional crystal structure [6,7,8,9, 10] opens up tempting prospects in creation of novel FIR and THz devices [11,12,13,14,15], in particular, novel photodetectors. One of the most promising metamaterials for FIR and THz detectors is a patterned graphene which constitutes an array of graphene nanoribbons (GNRs). The energy gap between the valence and conduction bands in GNRs as well as the intraband subbands can be engineered varying the shape of GNRs, in particular, their width, which can be defined by lithography. [16,17,18]. This opens up the prospects of creation of multicolor photodetectors.In this paper, we propose of a graphene nanoribbon phototransistor (GNR-PT) and evaluate its performance using the developed device model. The detector proposed has a structure of GNR field-effect transistor consisting of an array of GNRs with the side source and drain contacts (to each GNR) sandwiched between the highly conducting substrate and the top gate electrode. The operation of devices with similar structure were explored recently (see, for instance, [17,18,19,20,21,22,23]). Here, we study The structure of GNR-PT under consideration is schematically shown in Fig. 1. For the sake of definiteness, we consider a GNR-PT with optical input from the bottom of the structure assuming that the substrate and the layer sandwiching the GNR array are transparent.Graphene nanoribbons exhibit the energy spectrum with a gap between the valence and conduction bands depending on the nanoribbon width d: