We calculate the evolution of massive stars, which undergo pulsational pair-instability (PPI) when the O-rich core is formed. The evolution from the main-sequence through the onset of PPI is calculated for stars with the initial masses of $80 - 140$ $M_{odot}$ and metallicities of $Z = 10^{-3} - 1.0$ $Z_odot$. Because of mass loss, $Z leq 0.5$ $Z_odot$ is necessary for stars to form He cores massive enough (i.e., mass $>40 ~M_odot$) to undergo PPI. The hydrodynamical phase of evolution from PPI through the beginning of Fe core collapse is calculated for the He cores with masses of $40 - 62 ~M_odot$ and $Z = 0$. During PPI, electron-positron pair production causes a rapid contraction of the O-rich core which triggers explosive O-burning and a pulsation of the core. We study the mass dependence of the pulsation dynamics, thermodynamics, and nucleosynthesis. The pulsations are stronger for more massive He cores and result in such a large amount of mass ejection such as $3 - 13$ $M_odot$ for $40 - 62 ~M_odot$ He cores. These He cores eventually undergo Fe-core collapse. The $64 ~M_odot$ He core undergoes complete disruption and becomes a pair-instability supernova. The H-free circumstellar matter ejected around these He cores is massive enough for to explain the observed light curve of Type I (H-free) superluminous supernovae with circumstellar interaction. We also note that the mass ejection sets the maximum mass of black holes (BHs) to be $sim 50$ $M_{odot}$, which is consistent with the masses of BHs recently detected by VIRGO and aLIGO.
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