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A robot system used for minimally invasive surgery (MIS) has been developed in this paper. The system contains a surgeon console and a patient cart which is a surgical robot with two manipulators. By using the two master hands of the console, the surgeon can control the instruments and the arms to complete the operation accurately. In this paper, we mainly focused on the design and optimization of the robot arm. Based on the considering of the actual requirements of the minimally invasive surgery, incision positioning and instrument positioning mechanisms has been designed, which have seven degree of freedom in all and can provide enough workspace for MIS operation. According to the characteristics and actual movement of the surgical robot, the forward and inverse kinematics was also analyzed. Moreover, to make sure the robot has a good dexterity degree and high operable performance, the dexterous index is constructed by using the singular value of the Jacobian matrix and an optimization model was build. The robot's structure parameters were optimized by using sequential quadratic programming.