The time-resolved magneto-optical Kerr effect technique has been exploited to study the magnetization dynamics over femtosecond to nanosecond timescale for Gd-Fe thin films with different thicknesses. The precessional magnetization dynamics is studied by varying the magnitude and orientation of the bias magnetic field from nearly in-plane to nearly out-of-plane (OOP) direction. The analysis of bias magnetic field dependence of precessional frequency has revealed the development of OOP anisotropy when the film thickness was increased from 20 to 100 nm and this is in good agreement with the static magnetic properties of the films. Moreover, the 100-nm-thick film has shown a signature of perpendicular standing spin wave modes along with the uniform Kittel mode. The evolution of their frequency, decay time, and damping with the magnitude and orientation of bias magnetic field is analyzed in detail, showing possible energy transfer between the perpendicular standing spin wave modes and the uniform Kittel mode. Interestingly, the effective damping could be tuned over a broader range of 0.02 to 0.15, which shows the potential for applications in miniaturized and fast magnetic storage, magnetic memory, and magnonic devices. © 2019 American Physical Society.