We theoretically investigate the unconventional superconductivity in the newly discovered infinite-layer nickelates Nd$_{1-x}$Sr$_{x}$NiO$_{2}$ based on a two-band model. By analyzing the transport experiments, we propose that the doped holes dominantly enter the Ni $d_{xy}$ or/and $d_{3z^{2}-r^{2}}$ orbitals as charged carriers, and form a conducting band. Via the onsite Hund coupling, the doped holes are coupled to the Ni localized holes in the $d_{x^{2}-y^{2}}$ orbital band. We demonstrate that this two-band model could be further reduced to a Hund-Heisenberg model. Using the reduced model, we show the non-Fermi liquid state above the critical $T_{c}$ could stem from the carriers coupled to the spin fluctuations of the localized holes. In the superconducting phase, the short-range spin fluctuations mediate the carriers into Cooper pairs and establish $d_{x^{2}-y^{2}}$-wave superconductivity. We further predict that the doped holes ferromagnetically coupled with the local magnetic moments remain itinerant even at very low temperature, and thus the pseudogap hardly emerges in nickelates. Our work provides a new superconductivity mechanism for strongly correlated multi-orbital systems and paves a distinct way to exploring new superconductors in transition or rare-earth metal oxides.
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