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

Orbital Selective Superconductivity in Two-Orbital Asymmetric t-J Models