Pertaining to the past twenty years, research on the movement control of Autonomous Underwater Vehicles (AUVs) has become a significant point because of their wide scope of utilization in different fields like environmental research, security patrol, surveillance, rescue, etc. In this paper, velocity tracking problem of a new Bio-mimetic (Biologically inspired) AUV in a horizontal plane and depth-pitch tracking is addressed. Bio-mimetic AUVs (BAUVs) strives to enhance performance in diverse ocean conditions. The performance parameters like speed, efficiency, maneuverability, and stealth are remarkable compared to conventional AUVs. The proposed modeling approach is based on the kinematics and dynamic equations of marine vehicles. A conventional Proportional-Integral-Derivative (PID) controller with different tuning methods is used in this work for motion controlling purposes. Later on, a robust control method is presented to achieve better performance.