A high-resolution and high-accuracy optical vector analysis based on optical double-sideband modulation and stimulated Brillouin scattering is proposed and experimentally demonstrated. Different from the conventional OVA based on optical single-sideband modulation, in which the measurement range is limited by the bandwidth of the microwave and optoelectronic components, and the measurement accuracy is restricted by the high-order sidebands, the proposed technique measures the magnitude and phase responses by making use of both ±1st-order sidebands without spectrum response aliasing. As a result, the measurement range is doubled, and the high-order, sideband-induced errors only appear at specific frequencies that are predictable and removable. A proof-of-concept experiment is carried out. The transmission response of a fiber Bragg grating, in a range of 80 GHz, is measured with a resolution of less than 667 kHz by using 40 GHz microwave components.