We present the principle and the experimental verification of a distance measurement method based on the propagation of terahertz waves. The method relies on modulating the amplitude of a resonant-tunneling-diode (RTD) oscillator used as terahertz-wave source and on measuring the phase of the detected wave by applying a quadrature mixing technique. The distance measurement is found to have a residual error as small as 0.063 mm (standard deviation), which is a record for an RTD-based terahertz-wave radar system. This is almost five times better than our previous record of 0.29 mm, when an oscilloscope was used for phase measurements; additionally, the quadrature mixing brings about numerous practical benefits, such as greatly reduced cost, size, weight, complexity, and power consumption.