A high strength galvanized steel sheet excellent in coating adhesiveness is made from a base material that is a high strength steel sheet containing Si, Mn, and Cr. A method includes performing an oxidation treatment on steel containing Si, Mn, and Cr in an oxidation furnace under the condition that a selected exit temperature T, reduction annealing and a galvanizing treatment, or optionally, further an alloying treatment under conditions that heating is performed at a temperature of 460° C. or higher and 600° C. or lower for an alloying treatment time of 10 seconds or more and 60 seconds or less.