To clarify the effect of steel strength on the frictional behavior during press forming, frictional coefficient and galling property were studied with cold rolled steel sheet. Frictional coefficient was measured by single sliding test. Critical contact pressure above which the frictional coefficient decreased sharply was observed to increase with the strength of steel. A repetitive sliding test under the same compressive force was introduced to evaluate galling property. It is shown that the galling property is controlled by the ratio of contact pressure to yield strength of steel, and the galling property of high strength steel is better than that of mild steel if the initial contact pressure is the same. It is also notable that galling property becomes better as the increase of frictional coefficient with the number of slide becomes smaller.