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Using generalized Huygens-Fresnel diffraction integration, the analytical expression of Hermite-Cosine-Gaussian beams propagating in a gradient-index medium is deduced, and the influence of the gradientindex medium on the propagation properties of Hermite-Cosine-Gaussian beams with this expression is discussed for digital simulation. The results show that when Hermite-Cosine-Gaussian beams propagating in a gradient-index medium, axial intensity emerges spatially cyclical changes and maximum intensity position is related to gradient-index factor β. With the increase of the modulation parameter α , axis maximum intensity decreases and the hollow distribution emerges. In the same propagating plane, with the increasing of the gradient index parameter β , the transmitted intenisty increases at first but then decreases rapidly. And with the increase of α , intensity strength keeps unchanged, but waist width becomes narrowed.

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