Electronic structures of the artificial molecule comprising two truncated pyramidal quantum dots vertically coupled and embedded in the matrix are theoretically analysed via the finite element method.When the quantum dots are completely aligned,the electron energy levels decrease with the horizontally applied electric field.However,energy levels may have the maxima at non-zero electric field if the dots are staggered by a distance of several nanometers in the same direction of the electric field.In addition to shifting the energy levels,the electric field can also manipulate the electron wavefunctions confined in the quantum dots,in company with the non-perfect alignment. Electronic structures of the artificial molecule comprising two truncated pyramidal quantum dots vertically coupled and embedded in the matrix are theoretically analyzed via the finite element method. Whilst the quantum dots are completely aligned, the electron energy levels decrease with the filed applied electric field. However, energy levels may have the maxima at non-zero electric field if the dots are staggered by a distance of several nanometers in the same direction of the electric field. In addition to shifting the energy levels, the electric field can also manipulate the electron wavefunctions confined in the quantum dots, in company with the non-perfect alignment.