In the measurement of pulsed neutrons in the MeV energy range, plastic scintillators are one of the most widely used materials, and their neutron energy spectrum responses are key data of pulsed neutron energy spectrum measurement. The neutron energy spectrum responses of ST401 plastic scintillators with 5 different thickness values ranging from 0.5 to 10 mm in an energy range from 0.5 MeV to 100 MeV are measured by using the time-of-flight (TOF) method on the white neutron source (WNS) beamline of the China Spallation Neutron Source (CSNS). The effects of in-beam gamma rays, the gamma flash produced slow component of scintillator, and the pulse width of the neutron source on the measurement of neutron spectrum response are analyzed. Owing to the boundary effect of the finite volume of the scintillator, the neutron energy spectrum response curves of ST401 with different thickness values present approximately logarithmic shape, and proton escape is the main reason for the deviation of the curve from linearity. The thicker the scintillator, the higher the neutron energy deviates from linearity.