High-energy ultrashort gamma-ray pulses can be generated via laser Compton scattering with 90° collisions at the UVSOR-II electron storage ring. As an applied study of ultrashort gamma-ray pulses, a new photon-induced positron annihilation lifetime spectroscopy approach has been developed. Ultrashort gamma-ray pulses with a maximum energy of 6.6 MeV and pulse width of 2.2 ps created positrons throughout bulk lead via pair production. Annihilation gamma rays were detected by a BaF2 scintillator mounted on a photomultiplier tube. A positron lifetime spectrum was obtained by measuring the time difference between the RF frequency of the electron storage ring and the detection time of the annihilation gamma rays. We calculated the response of the BaF2 scintillator and the time jitter caused by the variation in the total path length of the ultrashort gamma-ray pulses, annihilation gamma rays, and scintillation light using a Monte Carlo simulation code. The positron lifetime for bulk lead was successfully measured.