The binding energy and structures of the Be cations with H2 molecules are studied theoretically at the level of the MP2 method. In this study, the aug-cc-pVTZ basis set is used to describe the electronic configuration of these atoms in these complexes. The structures of these complexes are determined for the \({Be}^{+}\bullet {\left({H}_{2}\right)}_{1-3}\) complexes. A tee and a vee shaped structure are obtained for mono- and di-ligated complexes, respectively. The tri- ligated complex is found to have trigonal prism geometry. The sequential bond energies of the \({Be}^{+}\bullet {\left({H}_{2}\right)}_{1-3}\) complexes are also examined. Differences in the electrostatic interaction energies and repulsive forces among H2 ligands in these complexes could be the cause of the variety in the observed trend in sequential bond dissociation energy values.