As a space X-ray imaging mission dedicated to time-domain astrophysics, the Einstein Probe (EP) carries two kinds of scientific payloads, the wide-field Xray telescope (WXT) and the follow-up X-ray telescope (FXT). FXT utilizes Wolter-I type mirrors and the pn-CCD detectors. In this work, we investigate the in-orbit background of FXT based on Geant4 simulation. The impact of various space components present in the EP orbital environment are considered, such as the cosmic photon background, cosmic ray primary and secondary particles (e.g. protons, electrons and positrons), albedo gamma rays, and the low-energy protons near the geomagnetic equator. The obtained instrumental background at 0.5-10 keV, which is mainly induced by cosmic ray protons and cosmic photon background, corresponds to a level of ∼3.1×10 −2 counts s −1 keV −1 in the imaging area of the focal plane detector (FPD), i.e. 3.7×10 −3 counts s −1 keV −1 cm −2 after normalization. Compared with the instrumental background, the field of view (FOV) background, which is induced by cosmic photons reflected by the optical mirror, dominates below 2 keV.