We show that the transit-time effects in the high-electric-field region near the drain edge of the channel of a field effect transistor can increase the increment of plasma wave growth in the device channel. These electron transit-time effects might lead to the plasma wave instability in high-electron-mobility transistors (HEMTs) in the terahertz range of frequencies. We demonstrate that the self-escitation of plasma oscillations is possible when the ratio of the electron velocity in the field region, u(d) , and the gate lenght, L-g , is sufficiently large in comparison with the electron collision frequency in the gated channel, v, i.e u(d)/L-g > v/k, where Kis a constant. Hence, in contrast with the Dyakonov-Shur mechanism of plasma instability in HEMTs, the plasma instability associated with the mechanism under consideration can occur at fairly low values of the electron mobility in the gated portion of the HEMT channel.