  We classify the pairing symmetries of three-dimensional superconductivity in
the zinc-blende structure which can support an electronic environment to host
unconventional high temperature superconductivity, and calculate the pairing
symmetry in the presence of strong electron-electron correlation by the slave
boson mean-field approach. We find that the $d_{2z^2-x^2-y^2} \pm id_{x^2-y^2}$
pairing state, a three dimensional analogy of the $d\pm id$ pairing in a two
dimensional square lattice, is ubiquitously favored near half filling upon hole
doping in both single-orbital and three-orbital models. However, unlike the two
dimensional counterpart, the Bogoliubov quasiparticle spectrum of the three
dimensional state upholds the full $T_d$ point group symmetry and encompasses
point nodes along certain high symmetric lines.
