A hollowed-out cross-shaped meta-material structure is designed and fabricated in this work. A kind of conventional magnetic material which works at low frequency is used as the absorber substrate. The simulation results demonstrate that an absorber can reach an absorption of less than -10 dB in a range between 2 GHz and 4 GHz, and the absorption band is expanded by a 0.5 GHz when the meta-material structure is unloaded. The experimental results indicate that a similar absorption band appears between 2.5 GHz and 5.1 GHz, which is 0.48 GHz wider than meta-material structure and the absorption band is expanded by 23% when the depth of absorption band below -9 dB. Compared with the cross meta-material, the hollowed-out structure has ability to increase the magnetic energy loss and strengthen the coupling between the units. The influence of magnetic layer thickness on absorption capability of wave absorber is analyzed. The result indicates that the position of addition absorption band does not apparently move with variation in thickness of the magnetic material layer. Based on these results, two different meta-material structures are combined to obtain a wider absorber. The simulation result and the experimental result both show another 0.9 GHz expansion of the absorption band and it can also reduce the thickness of the magnetic layer.