A surface acoustic wave (SAW) filter structure was fabricated employing $4{mu}m$ thick nanocrystalline diamond (NCD) and $2.2{mu}m$ thick ZnO films on Si wafer. The NCD film was deposited in an $Ar/CH_4$ gas mixture by microwave plasma chemical vapor deposition method. The ZnO film was formed over the NCD film in an RF magnetron sputter using ZnO target and $Ar/O_2$ gas. On the top of the two layers, copper film was deposited by the RF sputter and inter digital transducer (IDT) electrode pattern (line/space : $1.5/1.5{mu}m$) was defined by the photolithography including a lift-off etching process. The fabricated SAW filter exhibited the center frequency of 1.66 GHz and the phase velocity of 9,960 m/s, which demonstrated that a giga Hertz SAW filter can be realized by utilizing the nanocrystalline diamond thin film.