In this paper, a robust optimisation approach is introduced for parameterising a thalamic neural mass model that simulates brain oscillations such as observed in electroencephalogram and local field potentials. In a previous work, the model was informed by physiological attributes of the Lateral Geniculate Nucleus in mammals and rodents; the synaptic connectivity parameters in the model were set manually by trial and error to oscillate within the alpha band (8–13 Hz). However, such manual techniques constrain modelling approaches involving a larger parameter space, for example towards exploring alternative parameter sets that may underlie similar brain states under different environmental conditions and owing to inter-individual differences. In this work, we implement a robust optimisation technique that is based on single-objective Genetic Algorithms, and incorporate newly devised objective and penalty functions for tackling the stochastic nature of the model input. Furthermore, a clustering algorithm is employed to identify robust and distinct parameter regions that will mimic spontaneous changes in thalamic circuit parameters under similar brain states due to environmental and inter-individual differences. The results from our study suggest that multiple robust and distinct parameter regions indeed exist, and the model shows consistent dominant frequency of oscillation within the alpha band corresponding to all of these identified parameter sets.