Abstract: A statistical correction method is proposed to suppress the pile-up background events in data analysis. This method is verified by a cosmic muon lifetime measurement experiment, achieved by a plastic scintillator detector using the timing coincidence method, where dominant background events originate from pile up muons and electronic noise. To complement the intrinsic shortcoming of relatively rare decay events from registered cosmic muon events in the local laboratory, Monte Carlo simulation is applied to generate large samples in order to cross check the new method. The measurement of the muon lifetime in our setup gives a result of \tau_\mu^\rm exp = 2.19 \pm 0.07 \ \mu \texts at 95% confidence level, while the result before applying the correction is \tau_\mu' = 2.27 \pm 0.07 ~\mu \texts (95% C.L.). The treatment of pile-up events by a statistical correction equation in this study might be adapted to improve data analysis in the general coincident background dominating experiments.