Based on sum-of-squares ( SOS) decomposition, we propose a new solution approach for polynomial linear parameter-varying (LPV) system analysis and control synthesis problems. Instead of solving matrix variables over positive cone, the SOS approach tries to find a suitable decomposition to verify the positiveness of given polynomials. The complexity of the SOS-based numerical method is polynomial of the problem size, and is computationally attractive. This approach also leads to more accurate solutions to LPV systems than most existing relaxation methods. Several examples have been used to demonstrate benefits of the SOS-based solution approach.