This paper investigates the application of pulse shape discrimination (PSD) technology in anti-coincidence measurements, aiming to utilize a BGO crystal integrated within the optical chamber of a liquid scintillation detector for background suppression. In this study, the Tail-to-Sum Ratio (TSR) method is employed to effectively distinguish liquid scintillation signals from BGO signals. The research is based on a Geant4-simulated liquid scintillation system response model: by collecting the arrival times of photons at the photomultiplier tube (PMT) photocathode, the light pulse response x(t) for a single nuclear radiation event is constructed. Based on this, the system response function h(t) of the liquid scintillation detector is built, and the output pulse function y(t) of the scintillation light pulse is obtained. A calculation method for the TSR reference value of the TSR value of y(t) is also proposed. The research results indicate that when using the TSR algorithm for pulse shape discrimination (PSD), the anti-coincidence measurement efficiency for cosmic ray muons can reach 95.06%. In addition, the calculated measurement errors for tritiated water and 14C activity at the optimal TSR level are 0.12% and 0.18%, respectively. Therefore, the TSR discrimination algorithm can effectively meet the design requirements for anti-coincidence measurements, demonstrating high accuracy and feasibility.