Graphene has remarkable characteristics that make it a potential candidate for optoelectronics and electronics applications. Graphene is a sensitive material that reacts to any physical variation in its environment. Due to its extremely low intrinsic electrical noise, graphene can detect even a single molecule in its proximity. This feature makes graphene a potential candidate for identifying a wide range of organic and inorganic compounds. Graphene and its derivatives are considered one of the best materials to detect sugar molecules due to their electronic properties. Graphene has low intrinsic noise, making it an ideal membrane for detecting low concentrations of sugar molecules. In this work, a graphene nanoribbon field effect transistor (GNR-FET) is designed and utilized to identify sugar molecules such as fructose, xylose, and glucose. The variation in the current of the GNR-FET in the presence of each of the sugar molecules is utilized as the detection signal. The designed GNR-FET shows a clear change in the device density of states, transmission spectrum, and current in the presence of each of the sugar molecules. The simulated sensor is made of a pair of metallic zigzag graphene nanoribbons (ZGNR) joint via a channel of armchair graphene nanoribbon (AGNR) and a gate. The Quantumwise Atomistix Toolkit (ATK) is used to design and conduct the nanoscale simulations of the GNR-FET. Semi-empirical modeling, along with non-equilibrium Green's functional theory (SE + NEGF), is used to develop and study the designed sensor. This article suggests that the designed GNR transistor has the potential to identify each of the sugar molecules in real time with high accuracy.