Space gravitational-wave detection is currently an international hotspot. The core technology is to measure the multi-degree-of-freedom motions between two test masses with a distance of few million kilometers. The test sensitivity needs to reach the level of ~1 pm/Hz^1/2 and ~1 nrad/Hz^1/2 within the frequency band of 1 mHz and 1 Hz. At present, laser interferometer is one of the most precise methods to achieve ultra-precision displacement measurement. In this paper, we introduce the ultra-precision multi-degree-of-freedom measurement using laser heterodyne interferometry for space gravitational-wave detection. The optical design, measurement principle, phase demodulation, and relative research progress at home and abroad are introduced. We also analyze the main noises of laser heterodyne interferometry in space gravitational-wave detection, and the current research of these noise sources are also introduced. Finally, the development trend and prospect of laser heterodyne interferometry for ultra-precision multi-degree-of-freedom measurement are forecasted.