Using the vibrating sample magnetometer and ex situ vector network analyzer ferromagnetic resonance, the static and dynamic magnetic properties of Tb (4 nm)/Cr (t(Cr))/Ni80Fe20 (12 nm) trilayers with different thickness of Cr layer (from 0.2 to 4.0 nm) were investigated comparing with those of Ni80Fe20 film. From the results of in-plane static magnetic hysteresis loops, we analyzed the soft magnetic properties and in-plane anisotropy, along with obtaining the saturation magnetization (M-s) which shows no obvious reducing and a modulation akin to RKKY coupling. By fitting the relationship of resonance field and linewidth versus resonance frequency, the effective magnetization 4 pi M-eff, gyromagnetic ratio gamma, and effective damping coefficient (alpha(eff)) were extracted. It is worthwhile to mention that the inserting of ultrathin Cr layer (0.2 nm) enhanced the above parameters obviously, which then backed down towards their values in Ni80Fe20 film with increasing the thickness of Cr layer as a result of the weakening magnetic proximity effect and the decreasing spin-pumping effect in trilayers. Finally, they became flattening with the Cr layer thicker than 1 nm where oscillations are also observed in the value of g and aeff. Interestingly, the oscillations in aeff and g are consistent with each other, which implies the damping mechanism mainly related to the spin-orbit coupling originating from the indirect interaction between Tb and Ni80Fe20. In addition, the inhomogeneous broadening (Delta H-0) were determined to be very small which further ascertain the accurate of the aeff.