Pulse shape discrimination of a liquid scintillator-based detector (BC501A) has been studied using a digital approach. The objective of this work is to develop a new neutron-gamma discrimination algorithm to improve the discrimination efficiency. The new approach is a combination of two parts. The first part uses an adaptive Sallen-Key filter to reduce noise in the pulse followed by traditional approaches of either charge comparison or time over threshold. The approach of adaptive Sallen-Key combined with time over threshold was found to have a much better capability to discriminate neutron events from that of gamma. The pulse shape discrimination performance obtained for a 5 inches by 5 inches (length by diameter) liquid scintillator detector using the combination of the adaptive Sallen-Key filter with time over threshold is found to be significantly higher compared to that obtained using traditional methods. Moreover, this combination has the potential for real-time hardware implementation.