A robot off-line programming method. The method includes: respectively obtaining a first data representing positions and orientations of the plurality of targets on at least one work piece, a second data representing position of the at least one work piece, a third data representing geometry of a tool, and a fourth data representing the tool position and orientation with respect to an end of the robot; obtaining the robot path for which the tool tip passes through the plurality of the targets on the at least one work piece; using a function of an inverse kinematics for the robot model in consideration of the first data, the second data, the third data and the fourth data, calculating how many of the targets on the obtained robot path are reachable to the tool in relation to various rotation angle of the tool around the tool axis within a predetermined range so as to comply with optimization criteria. With the automatic calculation and intuitive preview, users could get to know directly about how many targets can be processed actually on a robot path. If the reachability is unsatisfied, the users could also have chances to modify the settings to obtain a more reasonable and precise path. An apparatus for implementing the method is also disclosed.