This paper addresses an interesting switching strategy of gain-scheduled controllers for linear parameter-varying systems. Dividing a whole operating range into some small subranges which are covered with a set of convex hulls, we design gain-scheduled controllers via linear matrix inequalities for each subrange while using common Lyapunov function within each subrange but non-common over sub-ranges. We then switch from one gain -scheduled controller to another in an intersection of two neighbor convex hulls on-line. Although switching action tends to generate non-smooth control input, which may cause undesired behavior and even instability, the proposed method provides a unique perfectly smooth switching property to avoid such behavior. A design example of aircraft control is included.