Muon is the major cosmic rays at the sea level. It can be detected by scintillator detectors such as sodium iodide NaI(Tl). In paper, an experimental method is presented, which uses a high sampling rate oscilloscope to digitize the deposited signal of muon and the relevant decay signal, and the off-line analysis to determine the muon lifetimes. This experiment is relatively simple and can be extended as a frontier project for particle detection in college physics experiments, in which radioactive sources and conventional nuclear electronics are not essential.