In view of the requirements of X-ray detection in pulsar-based navigation, the performance of a soft X-ray detector based on electric field effect of graphene is studied. The formula of time resolution and energy resolution of the detector is given by theoretical calculation and COMSOL Multiphysics simulation software. When the soft X-ray of 5.9keV is incident on the silicon absorption layer, the theoretical value of the time resolution is about 7.2ns and the theoretical value of the energy resolution is about 90eV (1.5%). The results show that the detector can meet the basic requirement of X-ray detection in pulsar-based navigation.