Increasing demand for both accuracy and productivity in cell positioning highlights the need for automation process that integrates robotics and micro/nano manipulation technologies. Optical tweezers, which use low power laser beams to trap and manipulate particles at micro/nano scale, can be treated as special robot "end-effectors" to position biological objects in a noninvasive way. In this paper, we propose to use a robot-tweezer manipulation system for automatic transportation of biological cells. Computer vision is utilized to supply real-time positions of target cells. Dynamics equation of the trapped cell during the movement is analyzed. Closed-loop controllers are designed for transporting single cell as well as multiple cells. Experiments are performed on transporting live cells to verify the effectiveness of the proposed approach.