Traditional frequency modulated continuous wave (FMCW) laser ranging techniques are mostly implemented using tunable lasers or dual-light-source architectures. These systems are complex and difficult to engineer, and they suffer from error amplification in dynamic scenarios. To address these limitations, our research team proposed an FMCW laser ranging method based on electro-optic double-sideband (DSB) modulation. A frequency-stabilized laser and an electro-optic modulator are used to generate two oppositely swept frequency signals, which reduces the system size and mitigates dynamic errors. An all-phase fast Fourier transform (APFFT) algorithm was designed to achieve stable and reliable phase retrieval under highly dynamic and high-noise conditions. In addition, Kalman filtering was introduced to optimize dynamic state estimation and improve ranging stability. Experimental results show that, with a 20 m fiber link, the absolute distance measurement error of the proposed method does not exceed ± 20 μm. For a sinusoidally vibrating target with amplitude ≤ 500 nm and frequency ≤ 200 Hz, the relative displacement measurement error does not exceed ± 25 nm. These results verify the high reliability of the proposed method and provide strong support for promoting the engineering deployment of FMCW laser ranging technology.