A LaBr3:Ce scintillator has a high light output (similar to 60000 p.e/MeV) and a short decay constant (<25 ns), which makes it good for time spectrometry. Compared with a BaF2 scintillator, it can bear a much higher count rate, and can be coupled to photomultipliers without using a quartz window. In this work, a positron annihilation lifetime spectrometer (PALS) consisting of two bulks of phi 25 mmx 25 mm LaBr3:Ce scintillator coupled to two XP20D0 photomultipliers, respectively, was built. A time resolution of FWHM=206 ps was measured for the PALS with a Co-60 source at the energy window for Na-22. With this spectrometer, a reasonable lifetime value tau=221+/-4 ps in a pure Si sample is obtained, which means that the utilization of LaBr3:Ce as the detector for a PALS is feasible.