The development of the field of reinforcement learning was based on psychological studies of the instrumental conditioning of humans and other animals. Recently, reinforcement learning algorithms have been applied to neuroscience to help characterize neural activity and animal behaviour in instrumental conditioning tasks. A specific example is the hybrid learner developed to match human behaviour on a two-stage decision task. This hybrid learner is composed of a model-free and a model-based system. The model presented in this thesis is an implementation of that model-based system where the state transition probabilities and Q-value calculations use biologically plausible spiking neurons. Two variants of the model demonstrate the behaviour when the state transition probabilities are encoded in the network at the beginning of the task, and when these probabilities are learned over the course of the task. Various parameters that affect the behaviour of the model are explored, and ranges of these parameters that produce characteristically model-based behaviour are found. This work provides an important first step toward understanding how a model-based system in the human brain could be implemented, and how this system contributes to human behaviour.