The response function and relative efficiency of a Φ50.8 mm×50.8 mm BC501A scintillator has been measured by using a252Cf fast fission chamber. In this method,a multi-parameter data acquisition system is employed to take the time-of-flight (TOF),pulse shape discrimination (PSD) and recoil energy (RE. note: fission neutron induces recoil proton while the prompt gamma ray induces Compton recoil electron) of the fission neutron and prompt gamma ray in an event-by-event mode with a TOF gate. The off-line data analysis method for separating the prompt gamma ray from the fission neutron as well as its contribution to the TOF spectrum and RE spectrum to obtain the relative efficiency and response function is discussed in detail. An accurate calibration of the effective neutron detection threshold is carried out by a linear extrapolation of the section around the point of inflexion in the relative efficiency plots using neutron energy directly. The relative efficiency with 0.51 MeV effective neutron detection threshold agrees with the Monte Carlo calculation result of NEFF. The response function from 0.5 MeV to 5 MeV generally agrees with the published experimental result of the NE213 scintillator of the same size.