The adsorption and reaction of cyclopentene on the Ge͑001͒ surface is investigated by first-principles density-functional calculations within the generalized gradient approximation. Surprisingly, a recent cluster calculation for adsorbed cyclopentene on Ge͑001͒ obtained an adsorption energy of 2.10 eV, which is larger than the same cluster result ͑1.65 eV͒ on Si͑001͒. However, our calculated adsorption energy for 0.5͑1͒monolayer cyclopentene on Ge͑001͒ is 0.79͑0.51͒ eV, comparable with an observed activation energy of 0.7 eV for desorption. In addition we find that the energy barriers for the adsorption of cyclopentene on Ge͑001͒ and Si͑001͒ not only depend on cyclopentene coverage but also quantitatively differ from each other. Based on the calculated energy profile for the reaction we discuss the experimental observations of the difference between cyclopentene sticking on the Ge͑001͒ and Si͑001͒ surfaces.