Oligodendrocyte precursor cells (OPCs) have remarkable properties: they represent the most abundant cycling cell population in the adult normal brain and they manage to achieve a uniform and constant density throughout the adult brain. This equilibrium is obtained by the interplay of four processes: division, differentiation or death, migration and active self-repulsion. They are also strongly suspected to be at the origin of gliomas, when their equilibrium is disrupted. In this article, we present a model of the dynamics of OPCs, first in a normal tissue. This model is based on a cellular automaton and its rules are mimicking the ones that regulate the dynamics of real OPCs. The model is able to reproduce the homeostasis of the cell population, with the maintenance of a constant and uniform cell density and the healing of a lesion. We show that there exists a fair quantitative agreement between the simulated and experimental parameters, such as the cell velocity, the time taken to close a lesion, and the duration of the cell cycle. We present three possible scenarios of disruption of the equilibrium: the appearance of an over-proliferating cell, of a deadless/non-differentiating cell, or of a cell that lost any contact-inhibition. We show that the appearance of an over-proliferating cell is sufficient to trigger the growth of a tumor that has low-grade glioma features: an invasive behaviour, a linear radial growth of the tumor with a corresponding growth velocity of less than 2 mm per year, as well a cell density at the center which exceeds the one in normal tissue by a factor of less than two. The loss of contact inhibition leads to a more high-grade-like glioma. The results of our model contribute to the body of evidence that identify OPCs as possible cells of origin of gliomas.