The "robotic-assisted liver tumor coagulation therapy" (RALTCT) system is a promising candidate for large liver tumor treatment in terms of accuracy and speed. A prerequisite for effective therapy is accurate surgical planning. However, it is difficult for the surgeon to perform surgical planning manually due to the difficulties associated with robot-assisted large liver tumor therapy. These main difficulties include the following aspects: (1) multiple needles are needed to destroy the entire tumor, (2) the insertion trajectories of the needles should avoid the ribs, blood vessels, and other tissues and organs in the abdominal cavity, (3) the placement of multiple needles should avoid interference with each other, (4) an inserted needle will cause some deformation of liver, which will result in changes in subsequently inserted needles' operating environment, and (5) the multiple needle-insertion trajectories should be consistent with the needle-driven robot's movement characteristics. Thus, an effective multiple-needle surgical planning procedure is needed. To overcome these problems, we present an automatic multiple-needle surgical planning of optimal insertion trajectories to the targets, based on a mathematical description of all relevant structure surfaces. The method determines the analytical expression of boundaries of every needle "collision-free reachable workspace" (CFRW), which are the feasible insertion zones based on several constraints. Then, the optimal needle insertion trajectory within the optimization criteria will be chosen in the needle CFRW automatically. Also, the results can be visualized with our navigation system. In the simulation experiment, three needle-insertion trajectories were obtained successfully. In the in vitro experiment, the robot successfully achieved insertion of multiple needles. The proposed automatic multiple-needle surgical planning can improve the efficiency and safety of robot-assisted large liver tumor therapy, significantly reduce the surgeon's workload, and is especially helpful for an inexperienced surgeon. The methodology should be easy to adapt in other body parts.