Pulsed VNAs enabling large dynamic measurement at a low pulse duty cycle are necessary for the characterization of active devices due to the overheating damage risk under continuous wave stimulation. In this paper, we proposed a pulsed microwave photonic vector network analyzer (p-MPVNA) based on direct sampling. With the broad system bandwidth of the p-MPVNA and undersampling technique, pulsed signals are received thru asynchronous wideband detection, and pulsed S-parameters are calculated thru vector superposition. In asynchronous wideband detection, the continuous spectrum of the pulsed signal is discretized into multiple frequency components. A low repetition rate optical pulse train undersamples the pulsed signal, and the discretized frequency components are aliased. The frequency components in the main lobe including most energy of the pulse signal are vector superimposed to calculate the pulsed S-parameter. The proposed p-MPVNA has a dynamic range decreases rate of 10log(duty cycle) when pulse duty cycle is below 10% , which is much slower than that of 20log(duty cycle) for classical narrowband detection. An experimental p-MPVNA is established for validation. A 6 to 18 GHz microwave amplifier is measured with continuous and pulsed power supply and the measured gain curves are consistent with the results from a commercial VNA. The system dynamic range decrease with pulse duty cycle is verified by the pulsed S-parameter measurement of a 10 GHz low pass filter under continuous and pulsed stimulation.