The present invention relates to a surface treatment composition comprising, on the basis of 100 wt % of the solid part of the composition, 20-40 wt % of a water-soluble polyurethane resin, 40-60 wt % of a silane-based sol-gel resin in which three types of silane compounds are cross-linked, 5-15 wt % of a curing agent, 0.5-1.5 wt % of a corrosion inhibitor, 0.1-1.0 wt % of a molybdenum-based compound, 1.0-3.0 wt % of a silane coupling agent; 1.0-2.0 wt % of an organometallic complex, 1.0-2.0 wt % of an acid scavenger, 0.1-1.0 wt % of an aluminum-based compound, and 1.0-2.0 wt % of a lubricant. A ternary hot-dip galvannealed steel sheet treated with a chromium-free surface treatment coating agent, according to an exemplary embodiment in the present invention, has excellent resistance to blackening, alkali and corrosion, and provides excellent effects without concern for problems, in chromium treatment, of additional equipment installation, an increase in manufacturing costs and environmental pollution.