High strength and high conductivity Cu-Nb microcomposites are with nano-structured Nb fibers and pure Cu matrix. Strength size effect has been observed. The rule of strength changing with the size of Nb filaments was analyzed by stress-strain curves. The characteristics of elastic modulus and nano-indention hardness varying with the thickness of Nb filaments are investigated by nanoindentation. It is shown that the measured value of strength is considerably higher than that obtained by ROM and the UTS of Cu-Nb increases exponentially with the decreasing of dNb. Moreover, the nano-indention hardness of Nb filaments also increases greatly as the size dreased. It is believed that electronic interface scattering associated with the mean free path of the electrons is the main factor of Cu-Nb conductivity.