Many heat transfer tubes are distributed on the tube plates of a steam generator that requires periodic inspection by robots. Existing inspection robots are usually involved in issues: Robots with manipulators need complicated installation due to their fixed base; tube mobile robots suffer from low running efficiency because of their structural restricts. Since there are thousands of tubes to be checked, task planning is essential to guarantee the precise, orderly, and efficient inspection process. Most in-service robots check the task tubes using row-by-row and column-by-column planning. This leads to unnecessary inspections, resulting in a long shutdown and affecting the regular operation of a nuclear power plant. Therefore, this paper introduces the structure and control system of a dexterous robot and proposes a task planning method. This method proceeds into three steps: task allocation, base position search, and sequence planning. To allocate the task regions, this method calculates the tool work matrix and proposes a criterion to evaluate a sub-region. And then all tasks contained in the sub-region are considered globally to search the base positions. Lastly, we apply an improved ant colony algorithm for base sequence planning and determine the inspection orders according to the planned path. We validated the optimized algorithm by conducting task planning experiments using our robot on a tube sheet. The results show that the proposed method can accomplish full task coverage with few repetitive or redundant inspections and it increases the efficiency by 33.31% compared to the traditional planning algorithms.