Logic computing in magnetic domain walls is investigated using the interplay of all-optical helicity-dependent switching and current-induced spin-orbit torque switching. By simultaneously controlling current and laser pulses, logic functions of AND, OR, NAND and NOR are experimentally demonstrated through anomalous Hall effect. The optoelectronic domain-wall motion is energy-efficient compared to the traditional all-current approach and provides another degree of freedom for the realization of logic applications.