A neutron detector array is one of the essential detector components for measuring the nuclear symmetry energy in the large-acceptance multipurpose spectrometer (LAMPS) to be built at the new radioactive ion-beam facility, RAON, in Korea. We have designed and built a real-size prototype neutron detector for the LAMPS and investigated its performance with radiation sources. The intrinsic time resolution of the prototype modules estimated by using 60Co is about 1 ns. The neutrons and the gammas from 252Cf are clearly separated in the time spectra. The kinetic energy spectrum of the fission neutrons from 252Cf has been reconstructed and compared to the empirical Watt function. The result demonstrates that the current prototypes can detect neutrons with kinetic energies larger than about 6 MeV.