Under paraxial approximation,using gen eralized Huygens-Fresnel diffraction integral,the propagation expressions of cosine-Gaussian beam through the left-handed materi al slab are got,and the influence of propagation properties of cosine-Gaussian beam due to the negative refractive i ndex of left-handed material slab and the modulation parameter of cosine-Gaussian beam is studied.The result s of the study show that: whether in the left-handed materials slab or image space,the location of the a xial maximum light intensity is the position where cosine-Gaussian beam is focused,and the negative refractive index of the left-handed material slab will change the position of the cosine-Gaussian beam focusing.The negativ e refractive index will change the shape of the axial light intensity distribution in the internal of th e left-handed material slab,but it won′t change the shape of the axial light intensity distribution in image space .Whether in the internal of slab or image space,the modulation parameters of cosine-Gaussian beam can influence the a xial and transverse light intensities.