This paper presents gain optimization of a 6-DOF underwater robotic platform with 4 rotatable thrusters. To stabilize the 6-DOF motion of the underwater robotic platform, a back-stepping controller is designed with 6 proportional gains and 6 derivative gains. The 12 gains of the backstepping controller are optimized to decrease settling time in step response in 6-DOF motion independently. Stability criterion and overshoots are used as a constraint of the optimization problem. Trust-region algorithm and hybrid Taguchi-Random order Coordinate search algorithm are used to determine the optimal parameters, and the results by two methods are analyzed. Additionally, the resulting controller shows improved performance under disturbances.