Frequency-swept interferometry (FSI) is a well-known ranging technique, but it suffers from three problems, namely, the Doppler effect, the frequency-sweep nonlinearity, as well as the slow frequency-sweep rate. The first two problems hinder the measurement accuracy, while the third problem limits the measurement rate. In this paper, we present a dynamic FSI (DFSI) that solves these three fundamental problems simultaneously. The DFSI consists of two auxiliary interferometers (AU1 and AU2) and two measurement interferometers (FSI and frequency-fixed interferometry (FFI)). We use FSI to obtain the Doppler and nonlinearity affected ranging signal, AU1 to monitor the frequency-tuning nonlinearity in the frequency-swept laser (FSL), and FFI and AU2 to constitute a laser vibrometer for monitoring the target motion-induced Doppler effect. Then, a novel signal fusion processing technique is applied to reconstruct the real dynamic distance from the above-measured signals. The dynamic ranging error caused by the Doppler effect and frequency-sweep nonlinearity in FSI can be eliminated and the dynamic distance at each sampling point can be obtained. The validity of this method is demonstrated by numerical experiments.