This paper addresses on the design problem for a class of continuous-time linear systems under the saturated linear feedbacks. The concerned problem becomes an exponential stabilization one through the further refined treatment on the saturation nonlinearity, including a property of absolute value and the s-procedure lemma. Then, sufficient linear matrix inequality (LMI) conditions for its local exponential stabilizability are derived in the sense of Lyapunov stability criterion. A numerical example is provided to show the reduced conservatism of the proposed design conditions. (C) 2016 Elsevier Ltd. All rights reserved.