The eigenenergies of the low-lying energy levels of a two-dimensional quantum-dot helium are calculated. We have used the shifted 1/N expansion method to solve the relative part Hamiltonian of the quantum-dot helium for various values of coulomb to confinement energies ratio in a zero magnetic field. Based on comprehensive comparisons, the shifted method gives accurate energies compared with the corresponding ones obtained by perturbation, variational, full configuration interaction (FCI), Hartree-Fock (HF) and diagonalization methods.