A closed four-level system in atomic vapor is proposed, which is made to possess left handedness by means of the technique of quantum coherence. The method of density matrix is utilized in view of the rotating-wave approximation and the effect of local-field in dense gas. The result of the numerical simulation shows that the negative permittivity and negative permeability of the medium can be achieved simultaneously (i.e., the left handedness) in a wider frequency band under appropriate parameter conditions. Furthermore, when analyzing the dispersion property of the left-handed material, we find that the probe beam can be controlled to change from superluminal to subluminal or vice versa via changing the detuning of the probe field.