In order to study the influence of a left- handed material slab on the spot of sinh- Gaussian beams, the analytical expression of the spot is derived based on the generalized Huygens- Fresnel diffraction integral. Based on the expressions, the spot is calculated. The results show that when sinh- Gaussian beams propagates through left-handed material slabs, the focus position of spot size is the beam waist position which is influenced by the refractive index of left- handed material slabs, and waist width has nothing to do with the material of index of refraction; And it is similar that spot size of internal left-handed material slab and spot size of the phase space which are with eccentricity parameters changing rules is found. This study can be helpful to application of the light field manipulation.