In this paper，the structures and potential energy functions of the ground states of BeH, BeD, BeT molecules are investigated by quantum mechanical ab initio method in the level of QCISD(T)/aug-cc-pVTZ and CCSD(T)/6-311++G(3df，2pd). The spectroscopic data, ωe，ωeχe，Be，αe and De for the ground states obtained from the calculation are in good agreement with the data from experiment. It indicates that the potential energy functions of BeH, BeD, BeT can be expressed by the corrected Murrell-Sorbie functions.