We fabricated a fiber-optic alpha/beta detector, which is composed of a sensing probe, a plastic optical fiber, a photomultiplier tube, and a multichannel analyzer, to obtain the energy spectra of radioactive isotopes. As inorganic scintillators of a sensing probe, a ZnS(Ag) film was coupled with a $CaF_2$(Eu) crystal for alpha and beta spectroscopy. In this study, $^{210}Po$ and $^{90}Sr$ were used as alpha and beta sources, respectively, and we measured the radiation energy spectra using a fiber-optic alpha/beta detector to identify alpha and beta emitting radionuclides for nuclear medicine application. Also, the variations of energy spectrum were obtained according to the length of plastic optical fiber.