Based on the linear matrix inequality method, a new approach to the design of robust H2/H∞ controllers for linear systems with parameter uncertainties was proposed. The parameter uncertainties considered were assumed to be normbounded. By introducing a Lyapunov matrix to meet the H2 and H∞ performance constraints simultaneously for the resulting closedloop system, the robust H2/H∞ controller design was transformed into a convex optimal problem with constraints of linear matrix inequalities, to which the existing convex optimization techniques such as the interiorpoint algorithm can be applied. To show the effect of the proposed robust H2/H∞ controller, the dynamic responses of a quarter car model with an active suspension subjected to road surface irregular excitations, either as a stationary random process or as a discrete timehistory, were investigated. Numerical results show that whether the variation of the vehicle mass exists or not, the proposed robust H2/H∞ controller behaves very satisfactorily.