The invention relates to a laser welding method of a stainless steel sheet fillet weld and a clamp of the laser welding method. The laser welding method comprises the steps that four protective gas nozzles which are coaxial are used, argon serves as protective gas, demonstration location is conducted through a CCD sensor, visual locating by an operator is replaced, the included angle between a YW-52 welding head and the Z axis ranges from 25 degrees to 30 degrees, a horizontal sheet is in lap joint with the position at the two thirds of the thickness of a vertical sheet, the off-focus value ranges from +15mm to +25mm, the welding speed ranges from 2m/min to 6m/min, and laser welding is conducted. According to the laser welding method of the stainless steel sheet fillet weld, the precision and the speed of production are improved, sheet fillet weld fillet transition is achieved, the front surface and the back surface are not provided with oxidation tints, the welding quality can meet mass production, and the technical requirements of product design are achieved. In order to improve the efficiency and the quality of the welding method, when welding is conducted, the special clamp is applied. According to the welding clamp, one clamp body is in the horizontal position, the other clamp body is perpendicular to the clamp body in the horizontal position, and two 0.7mm sheets are fixed through the welding clamp. Through a rapid fixture, a gasket, pressing plates, a platform and screws, stainless steel can be rapidly located and firmly fixed, and the stainless steel can be prevented from being abraded in the process of fixing.