In the application control of industrial robot, the planning of its working trajectory is the key content of the system design. In order to make the welding robot perform welding efficiently according to the set trajectory and speed, the KUKA KR10 R1420 industrial robot is taken as the research object and its structure is analyzed. The coordinate system of each member was established by D-H parameter method, and the kinematics equation of the robot was established by homogeneous transformation matrix. The mathematical model of KR10 R1420 industrial robot was constructed by using MATLAB robot toolbox, and the trajectory planning and kinematics simulation were carried out. The stable and continuous trajectory of end-effector and the angle, angle velocity and angle acceleration curves of each joint were obtained. The simulation results verify the correctness and rationality of the kinematics model of KR10 R1420 industrial robot, which provides a reference scheme for welding robot of trajectory planning in the complex environment.