Abstract: Under paraxial approximation, the transfer matrix of left-handed slab focusing system is derived. Using ABCD law, the propagation expressions for Gaussian beam focused by a left-handed material slab are obtained. On the basis of propagation formula, the focusing properties of Gaussian beam are analyzed. The beam waist of image Gaussian beam is equal to the beam waist of object Gaussian beam under paraxial approximation, that is to say, the left-handed material slab can not focus Gaussian beam. The focusing for Gaussian beam with a left-handed material coincides with imaging rules of geometrical optics and does not have focal shift.