The Gran Telescopio Canarias (GTC) Adaptive Optics (AO) system, designed to work with Natural Guide Stars (NGS), is in its laboratory integration phase. The upgrade for the operation with a Laser Guide Star (LGS) has been approved, and the design of the LGS Facility is going to start. Hereafter we analyse the performance of a LGS AO system taking into account the GTC characteristics and error budget. Two scenarios are studied: launching the laser from the centre of the telescope aperture behind the secondary (on axis) and launching from the side of the primary mirror (off axis). The simulations have been performed using the Fractal Iterative Method (FrIM), a fast-reconstruction algorithm, with the parameters of the GTC for the telescope, the atmospheric profiles of the Observatorio del Roque de Los Muchachos (ORM), and data from the laser star unit developed by ESO.