Accurate measurement of the optical magnitude and phase responses based on optical single-sideband (OSSB) modulation with doubled measurement range is proposed and demonstrated. In the scheme, an optical carrier and a second-order sideband are generated by an RF signal at an OSSB modulator consisting of a Mach–Zehnder modulator and an optical bandpass filter. After the optical device under test, the signal is sent to a photodetector, generating a frequency-doubled microwave signal, which is mixed with the RF signal from the transmitter to generate another fundamental frequency signal for phase and magnitude extraction. As a result, the measurement range of the OSSB-based optical vector analysers is doubled. In a proof-of-concept experiment, the magnitude and phase responses of a fibre Bragg grating are accurately measured.