A new problem for the automated off-line programming of industrial robot application is investigated. The Multi-Goal Path Planning is to find the collision-free path connecting a set of goal poses and minimizing e.g. the total path length. Our solution is based on an earlier reported path planner for industrial robot arms with 6 degrees-of-freedom in an on-line given 3D environment. To control the path planner, four different goal selection methods are introduced and compared. While the Random and the Nearest Pair Selection methods can be used with any path planner, the Nearest Goal and the Adaptive Pair Selection method are favorable for our planner. With the latter two goal selection methods, the Multi-Goal Path Planning task can be significantly accelerated, because they are able to automatically solve the simplest path planning problems first. Summarizing, compared to Random or Nearest Pair Selection, this new Multi-Goal Path Planning approach results in a further cost reduction of the programming phase.