Redundant mechanical arms have been widely favored by everyone due to their wide movement space and high flexibility.〖JP〗 However, its solution of inverse kinematics is complex and computationally intensive. To solve this problem, a five-axis redundant industrial robotic arm is taken as an example. A positive motion model was established according to the D-H convention, and the joint motion sequence was determined according to the actual situation. The inverse motion solving model was established based on algebraic method, which reduced the complexity of the solution and the calculation results met the requirements of trajectory planning. The fifth-order polynomial function was used to verify the plan in the joint space. The results show that the joints run smoothly and there is no obvious mutation point, which can meet the working requirements of the robot arm.