We demonstrate a hybrid-electrode Pockels cell (HEPC) using a thin z-cut deuterated potassium dihydrogen phosphate (DKDP) crystal. The device is a reflective, longitudinally driven, longitudinally cooled Pockels cell, constructed with a plasma chamber providing the incident-side electrode and a silicon-substrate mirror serving the three purposes of a mirror, a back-side electrode, and a heat sink. The mirror and the DKDP are thermally coupled through a sub-millimeter, inert gas-filled gap. A time-multiplex pass-by driving method is proposed to favor low-voltage and fast-response operation. The experimental results support that the HEPC would be a competent device for high-energy and high-repetition-rate lasers.