We study spin transport through a suspended Cu channel by an electrical non-local 4-terminal measurement for future spin mechanics applications. A magnetoresistance due to spin transport through the suspended Cu channel is observed, and its magnitude is comparable to that of a conventional fixed Cu lateral spin valve. The spin diffusion length in the suspended Cu channel is estimated to be 340 nm at room temperature from the spin signal dependence on the distance between the ferromagnetic injector and detector electrodes. This value is found to be slightly shorter than in a fixed Cu. The decrease in the spin diffusion length in the suspended Cu channel is attributed to an increase in spin scattering originating from naturally oxidized Cu at the bottom of the Cu channel.