We calculated the electronic structure of double quantum-dot molecule with a generalized LCAO approach and the finite element method.Compared with real molecule,the quantum dot molecule can be in the form of covalent bonding or ionic bonding between the two same (or different) quantum dots under different conditions.The condition is related to the distance between the two quantum dots and the energy of each quantum dot.The effects of the potential and radius of the quantum dots on the electronic structure have also been studied with the finite element method.