This paper discusses a design problem of robust control systems with adaptive gain controllers for a class of uncertain linear systems. The uncertainties under consideration which are composed of matched part and unmatched one are bounded, but its upper bounds are unknown, and the proposed controller consists of a fixed gain controller and a variable gain controller. In this paper, on the basis of piecewise Lyapunov functions, we show sufficient conditions for the existence of the proposed robust control system with the adaptive gain controller. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed controller.