By analyzing dielectric cube with high permittivity based on dielectric resonator theory, a new approach to the analyzing of left-handed metamaterials simultaneously with negative permittivity and negative permeability is proposed. The approach indicates that dipoles with Lorentz-type resonance electromagnetic responses can realize negative effective parameters in their negative resonant region. The dipole originates from standing wave in high permittivity dielectric cube. By combining electric dipole with magnetic dipole together, the interaction between two kinds of dipoles will destroy the standing wave and realize a left-handed passband. Numerical simulations indicate that by combining dielectric cubes with same sizes but different permittivities together, the electric resonant frequency and the magnetic resonant frequency can be coincident. Finally, experiments are carried out to verify the feasibility of all-dielectric left-handed metamaterial constructed by this means.