Based on the closed-form propagation expression of Hermite-cosh-Gaussian beams passing through an unapertured thin lens, intensity distributions in focal region were studied. Focal shifts of the beams and dependences of maximal intensity position on decentered parameter were investigated. The results show that the relative focal shifts (absolute value) in TEM_(11)-mode Hermite-cosh-Gaussian beams increase with decreasing decentered parameter and Fresnel number, and tend zero with large Fresnel number. For TEM_(22)-mode Hermite-cosh-Gaussian beams the principal maximum intensity is located off the axis when the decentered parameter is smaller than 0.54 and on the axis when decentered parameter is greater than 0.54. When decentered parameter equals 0.54, the beam has double principal maximum intensity here. The intensity is more concentrated into the axis with greater decentered papameter. Dependences of the relative focal shifts in TEM_(22)-mode beam obtained using LW and GH methods on decentered parameter and Fresnel number coincide with that of TEM11-mode beam. However , there is quantitative difference between the results obtained using the two different methods.