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An optical vector network analyzer (OVNA) based on unbalanced double-sideband (UB-DSB) modulation with improved measurement accuracy is proposed and experimentally demonstrated. It is different from an OVNA based on optical single-sideband (OSSB) modulation in which one-to-one mapping between the optical and radio frequency responses is employed to measure the magnitude and phase responses of an optical component, the proposed technique measures the magnitude and phase responses by taking into consideration of the power of the other sideband through solving two equations that are associated with the UB-DSB modulation, thus the errors due to the residual power of the other sideband in an OSSB modulation based approach are completely eliminated. A mathematical model providing the transfer function of an optical component is derived. The measurement of a phase-shifted fiber Bragg grating and a linearly chirped fiber Bragg grating is performed. Comparing with the measured results based on OSSB modulation, obvious improvement in measurement accuracy is demonstrated.