Tinnitus, the perception of a sound in the absence of acoustic stimulation, is often associated with hearing loss. Animal studies indicate that hearing loss through cochlear damage can lead to behavioral signs of tinnitus that are correlated with pathologically increased spontaneous firing rates, or hyperactivity, of neurons in the auditory pathway. Mechanisms that lead to the development of this hyperactivity, however, have remained unclear. We address this question by using a computational model of auditory nerve fibers and downstream auditory neurons. The key idea is that mean firing rates of these neurons are stabilized through a homeostatic plasticity mechanism. This homeostatic compensation can give rise to hyperactivity in the model neurons if the healthy ratio between mean and spontaneous firing rate of the auditory nerve is decreased, for example through a loss of outer hair cells or damage to hair cell stereocilia. Homeostasis can also amplify non-auditory inputs, which then contribute to hyperactivity. Our computational model predicts how appropriate additional acoustic stimulation can reverse the development of such hyperactivity, which could provide a new basis for treatment strategies.