In this paper,the structure and dissociation energy of the ground state of GaH （D,T） is investigated by quantum mechanical ab initio method in the QCISD/6-311++G（3df,3pd） and QCISD（T）/6-311++G（3df,3pd） level. Based on the theory of atomic and molecular statics, the dissociation limit for the ground state （X1Σ+）　of GaH （D,T） is derived. The potential energy curve and relevant optical constants of this state are obtained by least square fitting to the Murrell-Sorbie function. All calculation results are in good agreement with the experimental data.