Positron annihilation lifetime (PAL) spectroscopy is a unique method to study defects and supermicropores in solid materials. Traditionally, the pulsed slow positron beam (accelerator system included) was used to measure the PAL spectrum for a single film with a thickness of several microns, which is more complicated, expensive, and has worse time resolution than a conventional PAL spectrometer. In this paper, we developed a new PAL spectrometer to measure a single piece of micron-thickness film using two lanthanum bromide (LaBr3) detectors, a specially designed plastic scintillator detector, and a fast digitizer, at a cost equivalent to that of a conventional PAL spectrometer. The reliability and time resolution (around 210 ps, comparable to that of a conventional PAL spectrometer) of this spectrometer were verified by testing samples with thicknesses range from 15 to 60μm. Due to the successful construction of the new PAL spectrometer, PAL spectroscopy can now be applied to a single piece of micron-thickness film for the first time without building an accelerator system.