A PET system with a positron lifetime measurement function includes: a first gamma ray detector configured to receive, from an imaging target containing a nuclide that goes into an excited state of a daughter nucleus by undergoing beta decay and that then, subsequently to emission of a positron resulting from the beta decay, emits a deexcitation gamma ray when transiting into a ground state of the daughter nucleus, three annihilation gamma rays resulting from the positron annihilating with an electron, the first gamma ray detector thereby detecting the three annihilation gamma rays； a second gamma ray detector configured to detect the deexcitation gamma ray； and a processor configured to derive, in three dimensions, a distribution state of the nuclide in the imaging target and to determine information on a positron lifetime in association with a derived distribution position.
