This work aims to investigate the characteristics of the H atom in the tetrahedral interstitial sites of 8f2, 4c1, 8f1, 4c2, 8e, and 8g1 in the ZrCoH3 cell by first principles calculation based on the density functional theory. The research shows that pressure can change the local property of the electrons and the bonding ability of the H atom and its adjacent metal atoms, resulting in changes in the stable point and the disproportion point of the H atom in ZrCoH3. Further research has found that at P = 0 GPa, the significant Co-H covalent bond makes the H atom prefer to occupy the tetrahedral interstitial sites of 8f1 and 4c2 in the ZrCoH3 cell, while the H atom occupying the tetrahedral interstitial site of 4c1 in the ZrCoH3 cell has a significant Zr-H ionic bond with its adjacent Zr atom, which is the reason for the disproportionation of the ZrCoH3 alloy. When P = 10 GPa, the H atoms become unstable in the 8f1 and 4c2 tetrahedral interstices of the ZrCoH3 crystal cell. The significant Zr-H ionic bond between the H atoms in the 8f1 tetrahedral interstice and their adjacent Zr atoms is the reason for the disproportionation of the ZrCoH3 alloy, and the significant Co-H covalent bond makes the H atoms preferentially occupy the 4c1 and 8g1 tetrahedral interstices.