As an important parameter for characterizing the magnetization dynamics, Gilbert damping constant a in a thin film or a multilayer is generally extracted from the linear fitting of the frequency-dependence of the ferromagnetic resonance linewidth, sometimes accompanied with a tiny deviation of the linewidth to a smaller value at the low-frequency or high-frequency region due to the two-magnon scattering with an in-plane-field configuration, in which an in-plane magnetic field H perpendicular to a microwave field h was applied in film plane during measurement. In contrast, here we report, in ultrathin Gd/Cr/Fe multilayers, an anomalously large linewidth in the film plane at the low-frequency region. For the first time, we have successfully extracted the Gilbert damping constant from perfect theoretical fitting to the experimental data, by considering the effective direction of the magnetization around in precession staying out of the film plane when the in-pane H at which the precession starts is below the saturation field. This magnetization deviation from the film plane is found to have an obvious contribution to the enhanced linewidth caused by two magnon scattering, while slightly reduce the intrinsic linewidth. Under the same resonance frequency, the deviation angle reaches the maximum values at t(Cr) = 1.0 nm while decreases when t(Cr) increases to 1.5 nm, which coincides with the trend of the surface perpendicular anisotropy constant K-perpendicular to. A reduced intrinsic damping constant alpha is obtained as the introduction of Gd layer and Cr layer as a result of the competition between the spin pumping effect and the interfacial effects at the Fe/Gd and Fe/Cr interfaces. While the decreasing alpha for film with Cr layer thickness increasing to 1.5 nm might means the contribution of the electron density of states at the Fermi energy n(E-F). This study offers an effective way to accurately obtain the intrinsic damping constant of spintronic materials/devices, which is essential for broad applications in spintronics.