This paper aims at reducing the insertion loss of surface acoustic wave (SAW) filters with constant group delay using Cu electrodes based on resonant single-phase unidirectional transducers (RSPUDTs). Theoretical analysis indicates that the reflectivity of a Cu-electrode/128°YX-LiNbO3 structure is about two times larger than that of an Al-electrode/128°YX-LiNbO3 structure of the same thickness. The high reflectivity of Cu electrodes is effective in increasing the variable range in the reflectivity, which provides more degrees of freedom in the optimization of RSPUDT. A constant-group-delay filter is designed and fabricated. Experimental results are in fairly good agreement with the design; group delay deviation of 30 ns is realized over the range of ±6.5 MHz at the center frequency of 490 MHz where the minimum insertion loss is 6.1 dB.