A novel approach to perform optical vector analysis (OVA) is proposed and experimentally demonstrated with carrier-shifted optical double-sideband (ODSB) modulation based on a dual-drive dual-parallel Mach-Zehnder modulator (DD-DPMZM). The proposed method has a doubled measurement range as compared with the conventional OVA based on optical single sideband modulation (OSSB), and a much simpler and more robust configuration as compared with the previously-reported ODSB-based OVA. In addition, the proposed scheme does not generate any undesirable spikes in the measurement results. The transmission response of a sampled 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. The influence of the unideal frequency-shifted optical carrier generation in the DD-DPMZM on the measurement error is also investigated.