Recently, the technologies of mobile robots have been growing rapidly in the fields such as cleaning robot, explosive ordnance disposal robot, patrol robot, etc. However, the researches about the autonomous underwater robots have not been done so much, and they still remain at the low level of technology. This paper describes a model of 3-joint (4 links) fish robot type. Then we calculate the dynamic motion equation of this fish robot and use Singular Value Decomposition (SVD) method to reduce the divergence of fish robot’s motion when it operates in the underwater environment. And also, we analysis response characteristic of fish robot according to the parameters of input torque function and compare characteristic of fish robot with 3 joint and fish robot with 2 joint. Next, fish robot’s maximum velocity is optimized by using the combination of Hill Climbing Algorithm (HCA) and Genetic Algorithm (GA). HCA is used to generate the good initial population for GA and then use GA is used to find the optimal parameters set that give maximum propulsion power in order to make fish robot swim at the fastest velocity.