This paper focuses on the feasibility of fast neutron energy spectrum measurement. The MCNPX and Geant4 are used to simulate two conversion models of stacking neutrons to protons in the triple GEM cathode coupled with multilayer polyethylene, with five kinds of single-energy neutron sources and Am-Be continuous neutron sources taken as research objects. The response function to 160 single energy neutrons and the recoil proton spectrum distribution of the above sources of the detection system are obtained by simulation. Using GRAVEL algorithm and MLEM algorithm and through simulation, the recoil proton spectra of six kinds of fast neutron sources are obtained, and they are further analyzed. The spectrum outcome is compared with the standard input spectrum, showing that they are in good agreement with each other. The relative uncertainty of the unfolding spectrum is around 10%–15%. In this part the relation of gas detector with the precision of unfolding spectrum is also discussed. The result shows that when the energy resolution of micro-pattern gas detection is better than 30%, the accuracy of fast neutron spectrum can meet the needs of practical applications. Furthermore, a new transformation model is proposed based on previous experiments and proves the feasibility of applying micro-pattern gas detector to fast neutron detection of simulation. Moreover, spectrum reconstruction can be achieved by using the obtained recoil proton spectrum combined with a suitable inversion algorithm. The modeling and spectrum analysis of this study can provide a different method of applying the fast neutron detection system composed of micro-pattern gas detectors to the detection of unknown fast neutron sources and also to the source recognition through spectrum reconstruction.