As the refractive index of the overlay is higher than that of the cladding, the Long Period fiber Grating (LPG) element exhibits high sensitivity. However, when the thickness of the overlay is tens of nanometers, the material of the overlay present a high absorption, and the absorption can impact the property of the LPG element. A numerical study based on the linearly polarized (LP) modes and the coupled-mode theory (CMT) is used for our research. The analyses mainly comprise the mode structure and the spectrum influenced by the transition intervals which include both the transition nearby and the transition apart. On the basis of the non-absorption ideal mode, we studied the transition and re-organization of the cladding modes caused by the absorption, as well as its impact on the spectrum of the LPG. The result shows that the absorption causes the sensitivity and the dynamic range of the LPG element changed. Finally, we present a new absorption LPG sensor element.