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This paper develops an optimal H∞ state feedback controller for a quarter-car active suspension system application. The plant parameters and performance requirements are borrowed from a prototype in the literature. The control design is done using convex optimization with linear matrix inequality constraints, which ensures a very fast and efficient computation of the controller, without trial and error procedures for control design. The results of the closed-loop system with the proposed controller prove to be attractive in terms of high attenuation of disturbances lying in the range of frequencies of typical disturbances for this application. Comparison with a controller from literature to cope with the same problem illustrate the superiority of the optimal H∞ controller. Moreover, for the parameters used in the paper, one of the gains of the controller can be made equal to zero, leading to a control implementation with no dependence on availability of the disturbance for feedback, which is very interesting from practical point of view, since the measurement of the disturbance, a difficult task, could be avoided in the control implementation. The evaluation of the closed-loop system on time and frequency show how the controller designed for optimal rejection of disturbances can be interesting for the application.