Propagating between the contacts of a field-effect transistor ͑FET͒, plasma waves in its channel can become unstable and lead to generation of terahertz radiation. While previous studies of this instability concentrated on rectangular FETs, alternative geometries present fresh opportunities. We studied theoretically plasma oscillations in a gated FET with Corbino geometry where, in contrast with the rectangular FET, the oscillations become unstable at symmetric boundary conditions. Moreover, their lowest eigenfrequency is almost twice as high as that in the rectangular FET at comparable instability increments. These advantages make the Corbino FET promising for practical realizations of terahertz oscillators.