Structure prediction studies on Ca-H binary systems under high pressures were carried out, and the structures of calcium hydrides in earlier works were reproduced. The previously unreported composition of CaH9 was found to be stable and experienced the phase transition series C-m -> P2(1)/m -> C2/m from 100 to 400 GPa. To the best of our knowledge, CaH9 may be the only alkaline earth hydride with an odd H content. At 400 GPa, the metastable R (3) over barm-CaH10 phase shares the same space group with the R (3) over barm-SrH10 phase with puckered honeycomb H layers. The C2/m phase of CaH9 and the R (3) over barm phase of CaH10 are excellent superconductors with T-c values of about 240-266 and 157-175 K at 300 and 400 GPa, respectively. The high contributions of H-derived states at the Fermi level play an important role in the superconductivity of calcium hydrides.