In a grating-coupled high-electron-mobility transistor, weak terahertz emission with wavelength around 400 m was observed by using a Fourier-transform spectrometer. The absolute terahertz emission power was extracted from a strong background blackbody emission by using a modulation technique. The power of terahertz emission is proportional to the drain-source current, while the power of blackbody emission has a distinct relation with the electrical power. The dependence on the drain-source bias and the gate voltage suggests that the terahertz emission is induced by accelerated electrons interacting with the grating.