The application of Tailor Rolled Blanks （TRB） is one of the most effective ways to achieve automobile lightening， however， it's difficult to join the materials with the variable thickness. The thickness of B340LA TRB ranges from 1.2 mm to 2.0 mm and fluctuates in both length and width directions. And its hardness has a maximal deviation of 20% at different thickness. The special welding fixture was designed based on characteristics of TRB， and step variable laser power was proposed. By a contrastive analysis of two laser welding tests， including constant laser power and step variable laser power， the results show that there are huge differences in the weld appearance and penetration status along the welding direction under the conditions of constant laser power（900~1 400 W），and the defect of surface depression occurs in a portion of weld. By step variable laser power with 1 000 W， 1 100 W and 1 300 W，approximately consistent weld appearance and penetration status were obtained in the direction of thickness from 1.2 mm to 2.0 mm， and the hardness deviation in fusion zone of weld is less than 9%. B340LA TRB can be joined more effectively by step variable laser power than by constant laser powers.