The potential energy curves (PECs) of the X(1)Σ(+), a(3)Σ(+), A(1)Π and C(1)Σ(-) electronic states of the SiO molecule are studied using an ab initio quantum chemical method. The calculations have been made employing the complete active space self-consistent field (CASSCF) method, which is followed by the valence internally contracted multireference configuration interaction (MRCI) approach in combination with several correlation-consistent basis sets. The effect on the PECs by the core-valence correlation and relativistic corrections is included. The way to consider the relativistic correction is to use the third-order Douglas-Kroll Hamiltonian approximation. The core-valence correlation correction is carried out with the cc-pCVQZ basis set, and the relativistic correction is performed at the level of the cc-pVQZ basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are also corrected for size-extensivity errors by means of the Davidson modification (MRCI+Q). The PECs of these electronic states are extrapolated to the complete basis set limit by the total-energy extrapolation scheme. Employing these PECs, the spectroscopic parameters are calculated and compared with those reported in the literature. With these PECs determined by the MRCI+Q/CV+DK+56 calculations, by solving the radial Schrödinger equation of nuclear motion, 110 vibrational states for the X(1)Σ(+), 69 for the a(3)Σ(+), 54 for the A(1)Π and 67 for the C(1)Σ(-) electronic state are predicted when the rotational quantum number J equals zero. The vibrational manifolds of the first 20 vibrational states are reported and compared with the available RKR data for each electronic state. On the whole, as expected, the most accurate spectroscopic parameters and molecular constants of the SiO molecule are obtained by the MRCI+Q/CV+DK+56 calculations. And the present molecular constants of the a(3)Σ(+), C(1)Σ(-) and A(1)Π electronic states determined by the MRCI+Q/CV+DK+56 calculations should be good prediction for future laboratory experiment.