The doping effect of hydrogen on the Ca3CHx (x = 1, 4, 7, 9, and 10) antiperovskite compounds has been examined using density functional theory (DFT). The results of the structural optimizations show that all these compounds have negative formation energy implying the energetic stability and synthesizability. The band structures that are essential for the electronic properties have been determined along with the partial density of states (DOS) showing the metallic behavior of these compounds. In addition, the electron-density distribution has been determined, and the charge of each ion in the structures has been obtained with the Bader partial charge analysis. Moreover, the electronic stability of these compounds has been determined using the band filling theory and the number of the electrons at the Fermi level. The results of the formation enthalpy and the electronic stability investigations imply that the most stable structure is Ca3CH among the considered compounds. Ca3CH10 has the gravimetric storage capacity as 7.10 wt% that is the largest capacity among the considered compounds. Also, Ca3CH9 has the smallest hydrogen desorption temperature as 468.4 K among the studied compounds.