This thesis explores the application of a biologically inspired adaptive controller to quadcopter flight control. This begins with an introduction to modelling the dynamics of a quadcopter, followed by an overview of control theory and neural simulation in Nengo. The Virtual Robotics Experimentation Platform (V-REP) is used to simulate the quadcopter in a physical environment. Iterative design improvements leading to the final controller are discussed. The controller model is run on a series of benchmark tasks and its performance is compared to conventional controllers. The results show that the neural adaptive controller performs on par with conventional controllers on simple tasks but exceeds far beyond these controllers on tasks involving unexpected external forces in the environment.