The emerging field of superconductor (SC) spintronics has attracted intensive attentions recently.Many fantastic spin dependent properties in SCs have been discovered, including large magnetoresistance, long spin lifetimes and the giant spin Hall effect, etc. Regarding the spin dynamics in superconducting thin films, few studies has been reported yet. Here, we report the investigation of the spin dynamics in a s-wave superconducting NbN film via spin pumping from an adjacent insulating ferromagnet GdN film. A profound coherence peak of the Gilbert damping of GdN is observed slightly below the superconducting critical temperature of the NbN, which agrees well with recent theoretical prediction for s-wave SCs in the presence of impurity spin-orbit scattering. This observation is also a manifestation of the dynamic spin injection into superconducting NbN thin film. Our results demonstrate that spin pumping could be used to probe the dynamic spin susceptibility of superconducting thin films, thus pave the way for future investigation of spin dynamics of interfacial and two dimensional crystalline SCs.