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The cross sections of complete fusion and incomplete fusion for the 9 Be + 197 Au system, at energies not too much above the Coulomb barrier, were measured for the first time. The online activation followed by an offline γ-ray spectroscopy method was used for the derivation of the cross sections. A slightly higher value of the incomplete fusion to total fusion ratio has been observed, compared to other systems reported in the literature with a 9 Be beam. The experimental data were compared with coupled channel calculations without taking into account the coupling of the breakup channel, and experimental data of other reaction systems with weakly bound projectiles. A complete fusion suppression of about 40% was found for the 9 Be + 197 Au system, at energies above the barrier, whereas the total fusion cross sections are in agreement with the calculations. PACS numbers: