Time-domain analysis (TDA) is useful for measuring optical devices along with a link and for diagnosing a long device. In this Letter, an optical vector analyzer with TDA capability is proposed and experimentally demonstrated. The key to realizing TDA is a low-coherence optical carrier, which is achieved by modulating an electrical broadband signal on a continuous-wave light via acousto-optic modulation. Then, optical single-sideband modulation and vector balanced detection are used to measure the total frequency response of multiple devices under test (DUTs). Through an inverse Fourier transform, the obtained DUT impulses are distinguished in the time domain. Finally, time-domain gating and Fourier transform are applied to extract the frequency response of each DUT. An experiment is performed in which a fiber link comprising three DUTs and an H 13 C 14 N gas cell with a breakpoint inserted is characterized. The frequency setting resolution is 5 MHz, and a time-domain resolution of 30.84 ns is proved, which can reach 14.881 ns in theory.