Abstract: Based on the generalized HuygensFresnel diffraction integral, the closedform propagation expressions for HermitecosineGaussian(HCsG) beams through a paraxial optical ABCD system are derived. The propagation expressions for HermitecoshGaussian(HChG), cosineGaussian(CsG) and HermiteGaussian(HG) beams are obtained readily as special cases of HCsG beams. As application examples, numerical calculations are performed for HCsG beams propagating in free space and focused by a thin lens. The calculated results are shown that HCsG beams can not preserve their shape, while propagating in free space and through a thin lens.