A spectroscopic analysis device based on Brillouin dynamic grating and its analysis method, which provides high resolution and large measuring range at the same time. The device includes a laser device (1), a fiber optic coupler device (2), a first fiber amplifier device (3), a first isolator (4), a first polarization controller (5), a second polarization controller (6), a single-sideband modulation modulator (7), a second fiber amplifier device (8), a second isolator (9), a third polarization controller (10), a single-mode fiber (11), a polarization beam splitter (12), a circulator (13), a photodetector (14), a data acquisition card (15), a fourth polarization controller (16) and a microwave source (17). The method utilizes the Brillouin scattering of two beams of pump light in optical fiber forming Brillouin dynamic gratings as the spectral element and achieve a sub-MHz resolution.