A new adaptive Type-2 (T2) fuzzy controller was developed and its potential performance advantage over adaptive Type-1(T1) fuzzy control was also quantified in computer simulation. Base on the Lyapunov method, the adaptive laws with guaranteed system stability and convergence were developed. The controller updates its parameters online using the laws to control a system and tracks its output command trajectory. The simulation study involving the popular inverted pendulum control problem shows theoretically predicted system stability and good tracking performance. And the comparison simulation experiments subjected to white noise or step disturbance indicate that the T2 controller is better than the T1 controller by 0-18%, depending on the experiment condition and performance measure.