In the paper, we propose a photonic-assisted fast broadband microwave vector network analyzer (FB-VNA) based on frequency modulated continuous wave (FMCW). A photonic recirculating frequency shift (RFS) loop is used to extend the bandwidth of optical FMCW. The bandwidth-extended optical FMCW beats with the continuous wave (CW) light to generate the broadband electrical FMCW, which serves as the incident signal of the device under test (DUT). The response signals of the DUT are modulated on the bandwidth-extended optical FMCW to perform de-chirping. After coherently beating the de-chirped light with the CW light, the broadband response signals of DUT are down-converted to a single-tone intermediate frequency (IF) signal carrying the frequency response of DUT, and the scattering parameters of DUT can be obtained. The single-tone IF signal relaxes the demand on the bandwidth and sampling rate of the electrical backend. Thanks to the RFS loop and the short period of FMCW, the measurement frequency range is highly extended and measurement speed is greatly accelerated at the same time, which can be applied in monitoring sudden changes of DUT features. A bandwidth multiplication of the FMCW from 6-18 GHz to 6-498 GHz is experimentally implemented. With available photodetectors (PDs) and Mach-Zehnder modulators (MZMs), a 6-54 GHz FB-VNA is demonstrated, and the S parameters of a 25-GHz low-pass filter (LPF) is measured within 6 μs. The sudden changes of S21 parameter of DUT simulated by fast adjusting the bias voltage of the MZM used for de-chirping are also characterized by the proposed FB-VNA. The sudden changes as short as 0.01 μs can be captured.