Magnesium alloys, as heat-sink materials, have great potential for the application of electronics, communication and computer industries due to their low density, excellent electromagnetic shielding and damping capacity, high specific strength. Meanwhile, the thermal conductive ability of unit mass is better compared to aluminum alloy. State of research and development on high thermal conductivity magnesium alloy is reviewed in this paper, and Mg-Zn, Mg-RE, Mg-Th and Mg-Mn alloys with excellent thermal conductivities are analyzed. The problems existing in the study and the research direction of future are forecasted for high thermal conductivity of magnesium alloys