Under the paraxial approximation and based on the generalized Huygens-Fresnel diffraction integral formula, the propagation expressions of three-dimensional intensity of sinh-squared-Gaussian beams in free space, in a left-handed material slab and after propagation through the left-handed material slab are derived, and the numerical calculation and analysis are performed with the expressions to explore propagation properties of the sinh-squared-Gaussian beams through the left-handed material slab. The results show that the influence of the left-handed materials on the axial and the transversal intensity distribution of sinh-squared-Gaussian beams makes the intensity exhibit symmetrical distribution. The negative refractive index of the left-handed material slab changes the position of the maximum intensity. The axial and the transversal intensity changes with different propagation distances and decentered parameters, which shows that the sinh-squared-Gaussian beams cannot remain the same during propagation. In practical applications, it is feasible to shape beams in the manner of adjusting the decentered parameter at different locations.