Theoretical expressions and numerical calculations of axial forces for a left-handed material sphere, exerted by a highly focused Gaussian beam, in the ray optics regime are presented. Comparison is made between a dielectric sphere and a left-handed material sphere. The position at which the maximal magnitude of the axis force occurs is determined by the beam and the sphere parameters. A very strong axial force can be obtained from a low refractivity of a left-handed material sphere, exerted by a highly focused Gaussian beam, which is hundred times larger than that of a dielectric sphere.