We have explored the occurrence of the spherical shell closures for superheavy nuclei in the framework of the relativistic Hartree-Fock-Bogoliubov (RHFB) theory and the shell effects in terms of two-nucleon gaps $\delta_{2n(p)}$. Although the results depend slightly on the forces used, the general set of magic numbers beyond $^{208}$Pb are predicted as Z=120, 138 for protons and N=172, 184, 228 and 258 for neutrons, respectively. Specifically the RHFB calculations favor the nuclide $^{304}$120 as the next spherical doubly magic one beyond $^{208}$Pb. As indicated by the self-consistent calculations, the occurrences of superheavy shell closures are essentially related with the violation and restoration of relativistic pseudo-spin symmetry. Further analysis imply that the shell effects are sensitive to both the values of scalar and nonrelativistic effective masses, which togetherwith the violation of the relativistic symmetry may interpret the origin of model deviations.