Phase space is one of the most important parameters used to describe beam properties.Computer tomography,as a method for reconstructing phase space and measuring beam emittance,has been used in many accelerators over the past few decades.In this paper,we demonstrate a transverse phase space reconstruction study in the Shanghai soft X-ray free electron laser facility.First,we discuss the basic principles of phase space reconstruction and the advantage of reconstructing beam distribution in normalized phase space.Then,the phase space reconstruction results by different computer tomography methods based on the maximum entropy (MENT) algorithm and the filtered back projection algorithm in normalized phase space are presented.The simulation results indicate that,with proper configuration of the phase advance between adjacent screens,the MENT algorithm is feasible and has good efficiency.The beam emittance and Twiss parameters are also calculated using the reconstructed phase space.