Governor is a device used for maintaining a constant mean speed or rotation of the crank-shaft over long periods during which the load on the engine may vary. When the load of the engine decreases , the speed of the engine increases . As the spindle of the governor is driven by the engine , hence the speed of the spindle also increase. This will increase the centrifugal force on the governor balls and the balls moves outwards. Due to the movement of balls outwards the sleeve rise upwards. The upwards movement of the sleeve will operate a throttle valve at the other end of the ball crank lever to reduce the supply of the working fluid by reducing the throttle valve opening. similarly when the load on the engine increase, the speed of the engine decreases. Also the speed of the spindle of the governor decrease. Hence the centrifugal force on the governor balls will also decrease. The balls of the governor will move inwards and hence the sleeve will move downwards. The downwards movement of the sleeve will increase the supply of the working fluid by increasing the opening of the throttle valve and thus the engine speed is increased. Equation governing in this system is non-linear and one of the observing phenomenon results by non-linear approach is chaos.In this theses By using the fourth order Runge–Kutta numerical integration method, phase diagrams ,, Poincar’e maps, time history diagrams and power spectrum are presented to observe periodic , quasi-periodic and chaotic motions. The effect of the controlling parameter changes in the system can be found in the bifurcation diagram , largest lyapunov exponent and lyapunov dimentions. Finally three methods are used to control chaos effectively.