This paper presents the design of Model Reference Adaptive Control (MRAC) as tracking control system for unstable two input two output (TITO) Wheel Mobile Robot(WMR) system. MRAC technique is very much useful to track the desired trajectory for different SISO system. The novelty of this proposed controller is that it has been taken one TITO cross coupled WMR system, whose output responses are very much unstable. the uniqueness of this suggested control scheme is that its output responses can exactly track the reference input trajectory by comparing with the output response of the reference model which is an important part of MRAC structure and there is a scope for control designer to choose the appropriate reference model required for the WMR system. Adaptive control parameters needed for the control input in MRAC structure have been derived by Lyapunov theory and finally the dynamic characteristics of MRAC controlled TITO WMR have been compared with the State feedback and PID compensation to prove its efficiency as tracking control system in MATLAB simulink environment.