Femtosecond laser-triggered magnetization precession dynamics in exchange-coupled hard FePt/soft CoFe films has been studied by the time-resolved magneto-optical Kerr effect. The precession frequency is shown to be independent of the CoFe thickness tCoFe, while linearly proportional to the external field for the sample with tCoFe =7 nm, implying that the magnetization relaxation is governed by a uniform precession mode. The result agrees well with the theoretical prediction based on the Landau-Lifshitz-Gilbert equation. The obtained damping factor α∼0.13 is quite large and is thought to be dominated by the FePt layer. Additionally, the oscillation amplitude strongly depends on the CoFe thickness with a maximum value occurred at tCoFe =7 nm.