Optimization calculation is performed using different basis sets and methods for the ground state()of BeH molecule. Result show that the multi-reference configuration interaction(MRCI) method with aug-cc-pVQZ basis set for BeH molecule is the best group for calculating the equilibrium geometry, the dissociation energy. Potential energy curve(PEC) of BeH molecule have been computed by MRCI/aug-cc-pVQZ. Based on the analytical PEC, 12 vibrational states (J=0) of the ground state of BeH molecule are obtained by numerically solving the radical Schrdinger equation of nuclear motion. For each vibrational state, the vibrational energy levels , inertial rotation constants and the centrifugal distortion constants are calculated. Spectroscopic constants are obtained by fitting to vibrational energy levels and inertial rotation constants . Result show that the calculations are in good agreement with the experimental data.