The objectives of this study are to obtain a mathematical model for the passive and active suspensions systems for quarter car model. Current automobile suspension systems using passive components only by utilizing spring and damping coefficient with fixed rates. Vehicle suspensions systems typically rated by its ability to provide good road handling and improve passenger comfort. Passive suspensions only offer compromise between these two conflicting criteria. Active suspension poses the ability to reduce the traditional design as a compromise between handling and comfort by directly controlling the suspensions force actuators. In this study, the Linear Quadratic Control (LQR) technique implemented to the active suspensions system for a quarter car model. Comparison between passive and active suspensions system are performed by using different types of road profiles. The performance of the controller is compared with the LQR controller and the passive suspension system.