We present the zero-temperature superconducting (SC) ground states of the two-orbital asymmetric $t-J$ model on a square lattice by means of the auxiliary-boson approach. Besides the two-gap SC phase, we find an orbital selective SC (OSSC) phase, which is simultaneously SC in one orbit and normal in another orbit. The novel OSSC phase is stable only for sufficient asymmetric degree in orbital space and doping concentration. The pairing symmetry of the SC phase is s-wave-like in most doping regime, against the d-wave symmetry of the single-orbital $t-J$ model in a square lattice. The implication of the present scenario on multi-orbital heavy fermion and iron-based superconductors is also discussed.
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