The electrical resistivity of Cu/Ta multilayers deposited by radio-frequency magnetron sputtering on a polyimide substrate was investigated as a function of monolayer thickness. It is found that the resistivity of the multilayer increases with decreasing monolayer thickness from 500 nm to 10 nm. Two significant effects of layer interface scattering and grain boundary scattering were identified to dominate electronic transportation behavior in the Cu/Ta multilayers at different length scales. The electrical resistivity of the multilayer with monolayer thickness ranging from nanometer to submicron scales can be well described by a newly-proposed Fuchs-Sandheimair (F-S) and Mayadas-Shatzkes (M-S) combined model.