The invention relates to a laser and electric arc combined welding method for thick high-strength steel plates and a clamp for the method. A 45-mm thick high-strength steel is welded with a 6-KW fiber laser and through a double-sided welding forming method, small double-sided grooves are opened, and a 1mm-1.5mm gap is reserved, accordingly, the 45-mm thick high-strength steel can be completely welded. Compared with traditional multi-layer multi-pass welding which requires at least 20 passes of welding, the combined welding method has the advantages that the progress is apparent, preheating processes are simplified, preheating time is shortened, and welded joint performances reach client required indexes; the production efficiency is improved apparently, consumption of base metal and welding wires is reduced, energy consumption is decreased, the mechanical property of welded joints is improved, the residual stress and the deformation are reduced, automation of production can be easily achieved, and the like. The special clamp is a combined clamp with four pressing plates arranged on the upper portion and a base plate used on the lower portion during welding so as to improve the efficiency and quality of the welding method. By means of the clamp, a workpiece can be positioned and fixed, the welding quality is guaranteed, and the workpiece cannot be abraded.