Abstract: The plasma wave instability in rectangle field effect transistors (FETs) is studied with electron diffusion current density by quantum hydrodynamic model in this paper. General dispersion relation including effects of electrical thermal motion, external friction associated with electron scattering effect, electron exchange-correlation contributions and quantum effects were obtained for rectangle FETs. The electron diffusion current density term is considered for further analysis in this paper. It is found that the quantum effects, the electron diffusion current density and electrical thermal motion enhance the radiation power and frequencies. But the electron exchange- correlation effects and the electron scattering effects reduce the radiation power and frequencies. Results showed that a transistor has advantages for the realization of practical terahertz sources.