Based on the extended Huygens-Fresnel principle, the propagation expression of Hermite-cosine-Gaussian beam through the negative refractive index materials slab is derived and the numerical calculations are performed. The calculated results show that the negative refractive index of materials slab changes the position of the Hermite-cosine-Gaussian beam focusing, and the beam parameters of Hermite-cosine-Gaussian beam can affect the axial and transverse light intensities. However, the position of the maximum intensity is constant.