This paper deals with a strategy of gain optimization for the kinematic control algorithm of a wire-driven surgical robot. The proposed controller consists of the closed-loop inverse kinematics with the back-calculation method. The closed-loop inverse kinematics has 18 PID control gains, and the back-calculation method has 6 gains. An efficient strategy is designed to optimize 18 values first and then the remaining 6 values. The optimal gain sets are searched under the step input with performance indices. In this gain optimization, the objective function is defined as the minimum value of signal-to-noise ratio of the performance indices for 6 DoF (Degree-of-Freedom) motion that is based on the Taguchi method, and the constraints are applied to obtain stable responses for each motion evenly. The gain sets obtained are verified by simulations using the test trajectories. In comparative results, the optimal gain value based on the performance index combined with ISE (integral of square error) and settling time showed the best control performance.