A state feedback H_∞ controller design method for LPV systems based on smooth switching strategy is proposed to moderate the transient response of controllers switching. The range of time-varying parameters is divided into finite subspaces with overlapping regions. Using the Lyapunov function and projection theorem, the state feedback controllers are designed for subspaces. The controllers are adopted in non overlapping regions and weighted in overlapping regions of adjacent subspaces. Combined with the average dwell time method, the system satisfies global uniform exponential stability. In addition, a subspace partition method with variable overlap rate is proposed. Finally, the effectiveness of the proposed method is verified by a simulation example.