The problem of balancing an inverted pendulum has been a benchmark problem in demonstrating various control design techniques. The principal reasons for it's popularity are its nonlinear and unstable characteristics. In this paper a single link inverted pendulum system has been chosen and adaptive control algorithm has been implemented for stabilization of the system so that pendulum is always maintained erected in its upright (inverted) position. Model Reference Adaptive Control (MRAC) method is implemented using MIT rule. Minimization of cost function is performed and system response has been observed for different adaption gain. After system modeling the whole process is done in MATLAB Simulink.