When the boundary conditions of the source and drain are asymmetric, the plasma waves may become unstable in the channel of a field effect transistor (FET). We use the quantum magnetohydrodynamic model to study the influence of the quantum Bohm potential, Fermi statistical pressure, and electron spin effects on the stability of THz plasma waves propagating perpendicular to the magnetic field in the FET. A dispersion equation governing the THz plasma oscillation is obtained. Numerical results have shown that the presence of spin effects has enlarged the instable range of β, enhanced the instability increment, and made the frequency of THz plasma waves larger. The research shows that nanometer FETs with spin effects have advantages in realizing practical terahertz radiation.