A hybrid pulse shape discrimination (PSD) method is presented that combines a charge-integration PSD method with a reference-pulses PSD method. The reference-pulses PSD method uses detailed knowledge of the average detector response to radiation. To obtain the reference pulses, many thousands of neutron and gamma-ray pulses were averaged in several pulse height regions. The average neutron and gamma-ray pulses were then used in the new PSD algorithm for classification of a large number of measured pulses. The reference-pulses PSD method is applied below 70 keVee (keV electron equivalent) while the standard charge-integration PSD method is used above 70 keVee. This new hybrid PSD method proves to be more accurate than the standard charge-integration PSD method alone for classification of neutrons and gamma rays. Specifically, the improvement is approximately 40% for neutrons in the smallest pulse height bin considered, which was between 23 and 30 keVee (corresponding to approximately 175 keV and 225 keV neutron energy deposited, respectively). For this pulse height bin, approximately 66% of the neutrons were correctly classified. The average number of correctly classified neutrons is approximately 82% for the hybrid PSD method between 23 and 100 keVee (corresponding to approximately 175 keV and 670 keV neutron energy deposited, respectively).