•A pose optimization method is presented to eliminate the redundant freedom along a given five-axis CNC tool path aiming at increasing the robot stiffness, resulting in improved machining accuracy.•A new frame-invariant performance index is proposed to evaluate the stiffness of the robot at a certain posture.•The redundancy elimination problem is formulated as a one-dimensional optimization problem in consideration of the constraints of joint limits, singularity avoidance and trajectory smoothness.•The one-dimensional optimization problem is solved by a simple discretization search algorithm. Industrial robot provides an optimistic alternative of traditional CNC machine tool due to its advantages of large workspace, low cost and great flexibility. However, the low posture-dependent stiffness deteriorates the machining accuracy in robotic milling tasks. To increase the stiffness, this paper introduces a pose optimization method for the milling robot when converting a five-axis CNC tool path to a commercial six-axis industrial robot trajectory, taking advantage of a redundant degree of freedom. First, considering the displacements of at least three points on the end effector of the robot, a new frame-invariant performance index is proposed to evaluate the stiffness of the robot at a certain posture. Then, by maximizing this index, a one-dimensional posture optimization problem is formulated in consideration of the constraints of joint limits, singularity avoidance and trajectory smoothness. The problem is solved by a simple discretization search algorithm. Finally, the performance index and the robot trajectory optimization algorithm are validated by simulations and experiments on an industrial robot, showing that the machining accuracy can be efficiently improved by the proposed method.