Based on the atomic and molecular reaction statics, the ground electronic states of CrH(X6Σ+), CrH+(5Σ+), CrH2+ (6Σ+) and their dissociation limits have been derived. Using density functional method (B3PW91), 6-311++G** basis sets for H and split valence polarization basis sets for Cr, the molecular equilibrium geometry and dissociation energies for CrH+(5Σ+) and CrH2+ (6Σ+) have been calculated. The analytical potential energy functions for CrH(X6Σ+), CrH+(5Σ+) and CrH2+ (6Σ+) are determined. The force fields and spectroscopic parameters have been worked out from these analytical potential energy functions. For the ground state of CrH+, the calculated results of Re, f2, f3, f4, Be, αe, ωe and ωeχe are 0.16200 nm, 1.52574 aJ/nm2, -7.81171 aJ/nm3, 28.61613 aJ/nm4, 6.71181, 0.28792, 1624.6297 and 53.55394 cm-1, respectively; and for the ground state of CrH2+, the corresponding parameters are 0.24005 nm, 0.42946 aJ/nm2, -0.97766 aJ/nm3, 2.40438 aJ/nm4, 2.9562, 0.050184, 858.059 and 6.46813 cm-1, respectively. The theoretical results show minimum points in the potential energy curves of CrH+(5Σ+) and CrH(X6Σ+), so we conclude that CrH(X6Σ+) and CrH+(5Σ+) are stable.But there are no minimum points in the potential energy curves of CrH2+ (6Σ+), so CrH2+ (6Σ+) is not stable.