Frequency modulated continuous wave (FMCW) laser ranging offers high accuracy and stability, making it valuable for aerospace measurement and related fields. Conventional FMCW systems typically rely on tunable lasers or dual-source architectures, which increases system complexity and engineering difficulty, and they suffer from error amplification in dynamic scenarios. To address these issues, we propose an FMCW laser ranging method based on electro-optic double sideband modulation. A single-frequency laser combined with an electro-optic modulator generates two oppositely chirped signals, reducing the system footprint and canceling motion-induced dynamic errors. In addition, an all-phase fast Fourier transform algorithm is designed to deliver stable and reliable phase estimation under high-dynamics and high-noise conditions. A Kalman filter is further introduced to optimize dynamic state estimation and ?improve ranging stability. Experimental results show that, under long-range conditions with 20 m of inserted optical fiber, the absolute distance measurement error does not exceed ±20 μm; for sinusoidal vibration targets with amplitude ≤500 nm and frequency ≤200 Hz, the measurement error does not exceed ±30 nm, which verifies the high reliability of the proposed system in both absolute distance and relative displacement measurements.