Copper-doped SrBi2Nb2O9 (SBN) thin films have been fabricated on fused quartz substrates at room temperature by RF magnetron sputtering technique. The chemical composition and Cu concentration in the deposited films were characterized by X-ray fluorescence spectrometer. XRD analysis indicated that the films have a single phase of layered perovskite structure and Cu doping in SBN films did not degrade their crystallinity at the dopant concentration of 9.5%. The nonlinear optical properties of the samples were determined using a single beam z-scan technique at a laser wavelength of 532 nm with laser duration of 25 ps. The results showed that the value of $\chi ^{(3)}$ of Cu-doped SBN films is about twice larger than that of the undoped, which is comparable with that of some representative nonlinear optical materials, indicating that metal-doping in dielectric is effective to enhance their nonlinear optical properties. This suggests that Cu-doped SBN films have great potential in designing nonlinear optical devices.