Chromium hydride is a prototype stoichiometric transition metal hydride. The phase diagram of Cr-H system at high pressures remains largely unexplored due to the challenges in dealing with the high activation barriers and complications in handing hydrogen under pressure. We have performed an extensive structural study on Cr-H system at pressure range 0 ∼ 300 GPa using an unbiased structure prediction method based on evolutionary algorithm. Upon compression, a number of hydrides are predicted to become stable in the excess hydrogen environment and these have compositions of Cr2 Hn (n = 2-4, 6, 8, 16). Cr2 H3, CrH2 and Cr2 H5 structures are versions of the perfect anti-NiAs-type CrH with ordered tetrahedral interstitial sites filled by H atoms. CrH3 and CrH4 exhibit host-guest structural characteristics. In CrH8, H2 units are also identified. Our study unravels that CrH is a superconductor at atmospheric pressure with an estimated transition temperature (Tc) of 10.6 K, and superconductivity in CrH3 is enhanced by the metallic hydrogen sublattice with Tc of 37.1 K at 81 GPa, very similar to the extensively studied MgB2.