An optical vector analyzer (OVA) based on symmetric optical double-sideband (ODSB) modulation using a phase modulator (PM) and an intensity modulator (IM) is proposed and demonstrated. In the symmetric-ODSB-based OVA, frequency response measurements are implemented by transmitting the phase-modulated and intensity-modulated ODSB signals through an optical device-under-test (DUT), respectively. Then, removing the responses of the two electro-optic modulators and processing the measured responses, accurate frequency responses of the DUT on both sides of the optical carrier are obtained. Comparing with the conventional OVA based on optical single-sideband (OSSB) modulation, the proposed ODSB-based OVA has the doubled measurement range and the simple wavelength-independent configuration. Moreover, the measurement system inherently has large dynamic range and high accuracy, which is difficult to achieve for the OSSB-based OVA due to the restriction of the limited sideband suppression ratio. An experiment for measuring the magnitude and the phase responses of a programmable optical filter is carried out. The responses in a range of 100 GHz are measured with a resolution of 10 MHz by using 50-GHz components.