The ground (1 (2) Sigma(+), X) and excited electronic states, 1 (2) Pi (A), 2 (2) Sigma(+) (B,B’), 1 (2) Delta, 2 (2) Pi (E), 3 (2) Sigma(+) (D), 4 (2) Sigma(+) (C), 5 (2) Sigma(+) (K), 3 (2) Pi (L), and 2 (2) Delta, of CaH are studied by ab initio calculation, with extensive configuration interactions. Calculated spectroscopic constants, in particular, the excitation energies, are more accurate than in previous calculations and agree well with the currently available experimental data. This work confirms the existence of a single vibrational level, v’=4, bound to the second well of the B state calculated from the experimental data by Martin [J. Chem. Phys. 88, 1797 (1988)]. Calculated oscillator strengths for the B-X and D-X show irregular band structures because of multiple avoided crossings of the potential energy curves. The avoided crossing between the D and C states should be taken into account to explain the apparent perturbations observed in the experimental spectra. The wave functions, dipole moments, and transition dipole moments of these states are discussed in detail.