In this paper, a fast constrained model predictive control algorithm was designed for the active suspension of a half-car model to increase the controller bandwidth so that high frequency displacement disturbance coming from the road can be rejected. To this end, a quasi-LTI model of a semi-active suspension model was controlled by a model predictive controller with orthogonal Laguerre polynomials. With the use of Laguerre polynomials, it has been shown that the optimization parameter set could be made minimal, and thereby it has been shown that on-line optimization takes less time. With numerical simulations, it has been shown that the time complexity of a model predictive control having Laguerre polynomials is linear in the length of prediction horizon, whereas time complexity of a regular model predictive control is quadratic in the length of prediction horizon. Since it has been shown that time complexity of the constrained model predictive controller with orthogonal Laguerre polynomial is reduced, it is possible to extend the prediction horizon to large values. Further, constraints on the input signal and the state vector were also discussed within this context.