The invention relates to a square steel concrete composite column structure and an installation method thereof, and belongs to the technical field of building. The structure includes an inner square steel column, an outer square steel column, a reinforced concrete structure, an inner column fixed plate and composite connectors; the inner square steel column is located inside the outer square steelcolumn, and the edges of the inner square steel column and the edges of the outer square steel column are in 45-degree staggered arrangement; four corner edges of the inner square steel column are connected with the inner column fixed plate in the vertical direction at equal distance, and connection points of the exterior of the inner fixed plate are provided with bolt connecting holes; the middle parts of four side faces of the outer square steel column are uniformly provided with fixed plate reserved holes in the vertical direction at equal distance and correspond to the inner column fixedplate; a cast-in-place reinforced concrete structure is arranged between the inner square steel column and the outer square steel column; the square steel concrete columns are mechanically connected through the composite connectors. The advantages of the steel structure and the concrete structure are combined, and the square steel concrete composite column structure has the advantages of good integrity, good tensile and compressive performance, high bearing capacity, good plasticity and toughness, good seismic performance and convenient assembly, and can be assembled into a special-shaped column.