We study a Bose-Einstein condensate trapped by a ladder lattice in a high-fitness cavity. The ladder lattice is loaded in the x\text-y plane and the cavity is along the x direction. A pump laser shines on atoms from the z direction. Under the mean-field approximation, we consider the emergence of the quasi-periodic potentials induced by superradiance in the ladder lattice, which is described by \hatH_\textMF=\hatH_\textLad+\hatV_\texteff with the effective potential \hatV_\texteff(\alpha)=\displaystyle \sum\nolimits_i = 1^N\displaystyle \sum\nolimits_\sigma = 1,2\left\lambda_\rmD\cos(2\pi\beta i)+U_\rmD\cos^2(2\pi\beta i)\right\hatc^†_i,\sigma\hatc_i,\sigma. We find that the quasi-periodic potential can induce the reentrant localization transition and the regime with mobility edges. In the smaller U_\rmD case, the system exhibits a localization transition. The transition is associated with an intermediate regime with mobility edges. When U_\rmD goes beyond a critical value U_\rmD^(\rm c), with the increase of \lambda_\rmD, the system undergoes a reentrant localization transition. This indicates that after the first transition, some of the localized eigenstates change back to the extended ones for a range of \lambda_\rmD. For a larger \lambda_\rmD, the system experiences the second localization transition, then all states become localized again. Finally, the local phase diagram of the system is also discussed. This work builds a bridge between the reentrant localization and the superradiance, and it provides a new perspective for the reentrant localization.