The invention discloses nodes of a Y-shaped double-lug square tubular column and H-shaped steel beam columns, connecting pieces and a construction method. The nodes comprise the square steel tubular column, the four transverse H-shaped steel beam columns and the connecting pieces. Each connecting piece comprises a connecting assembly I and a connecting assembly II, the connecting assemblies I and the connecting assemblies II are located at the four corners of the square steel tubular column, and the intersected position of every two small fin plates is clamped to the edge of the square steel tubular column; an inverted trapezoid-shaped slot is formed between the two small fin plates of every adjacent connecting assemblies I, the connecting assemblies II correspond to the side walls of the square steel tubular column one to one, and base plates of the connecting assemblies II are embedded into the inverted trapezoid-shaped slots; a connecting plate is located between two connecting side plates, and the connecting plate and the connecting side plates are connected through bolts; and the contact portions of the connecting assemblies I and the edge of the square steel tubular column are connected in a welded mode, and the connecting assemblies II are welded to the ends of the H-shaped steel beam columns. According to the nodes of the Y-shaped double-lug square tubular column and the H-shaped steel beam columns, the connecting pieces and the construction method, standardization and productization of node connection are achieved, specific wedge-shaped self-tightening connecting construction of the nodes can prevent sliding between a steel beam and a steel column from occurring, and sliding stress is prevented from generating; and all machining is industrialized, and zero welding is conducted on the site.