Based on the general Huygens-Fresnel diffraction integral formula, the focal switch effect of Hermite-cosine-Gaussian beams passing through an astigmatic lens is investigated in detail. The results of numerical calculations show that this kind of focal switch is dependent of the geometric parameter of the optical system δ, and the focal switch effect occurs regardless of whether the δ is 1.0 or not, i.e. the focal switches could occur not only at geometric focus but also at the right or the left of the geometric focus. The influence of beam parameter on the occurrence and the position of focal switches is discussed. The dependence of the relative focal shift on the astigmatic parameter is examined at different geometric parameters of the optical system δ for a particular beam parameter and Fresnel number. The result shows that the occurrence and the position of focal switches can be controlled by changing the beam parameter and astigmatic parameter.