Tinnitus is often related to hearing loss, but how hearing loss could lead to tinnitus has remained unclear. Animal studies show that the occurrence of tinnitus is correlated to increased spontaneous firing rates of central auditory neurons, but mechanisms that give rise to such hyperactivity have not been identified yet. Here we present a computational model that reproduces tinnitus-related hyperactivity and predicts tinnitus pitch from the audiograms of tinnitus patients with noise-induced hearing loss and tone-like tinnitus. Our key assumption is that the mean firing rates of central auditory neurons are controlled by homeostatic plasticity. Decreased auditory nerve activity after hearing loss is counteracted through an increase of the neuronal response gain, which restores the mean rate but can also lead to hyperactivity. Hyperactivity patterns calculated from patients' audiograms exhibit distinct peaks at frequencies close to the perceived tinnitus pitch, corroborating hyperactivity through homeostatic plasticity as a mechanism for the development of tinnitus after hearing loss. The model suggests that such hyperactivity, and thus also tinnitus caused by cochlear damage, could be alleviated through additional stimulation.