The invention discloses a one-side support formwork structure for enlarging a section and strengthening construction and a construction method. The structure comprises a side formwork assembly, anchor ribs implanted in an original concrete wall surface and pulling and connecting assemblies pulled and connected between the side formwork assembly and the anchor ribs, a pouring space for pouring strengthened structures is formed between the side formwork assembly and the original concrete wall surface, and each pulling and connecting assembly is provided with a top formwork rib which abuts against the inner side of the side formwork assembly. According to the one-side support formwork structure for enlarging the section and strengthening construction and the construction method, due to the fact that the anchor ribs are implanted in the original concrete wall surface, the pulling and connecting assemblies are welded to the anchor ribs, side plate assemblies are pulled and connected to the anchor ribs through the pulling and connecting assemblies, and the pouring space for pouring the strengthened structures is formed between the side formwork assembly and the original concrete wall surface, the difficulty of strengthening of the one-side support formwork structure in the strengthening project can be solved by means of matching of the anchor ribs and the pulling and connecting assemblies, and meanwhile the pulling and connecting strength of the side plate assemblies and the original concrete wall surface is improved.