We applied the resistance spot welding with cover plates to high strength magnesium alloys Mg_<96>Zn_2Y_2. The cover plates is to keep a heat to welding area for spot welding of the high thermal conductivity materials. The welded specimen Mg_<96>Zn_2Y_2/Mg_<96>Zn_2Y_2 exhibited tensile share strength more than 750N at the welding current of 1880A. Mg_<96>Zn_2Y_2/SUS304 exhibited a high tensile share strength more than 1200N at the welding current of 1980A. The Vickers hardness of weld area is about 10 higher than that of base metal. High hardness of nugget is considered to be originated from the fine long period stacking order (LPSO) phase dispersion observed by cross-section transmission electron microscope.