Both Takagi-Sugeno and polynomial fuzzy model use the well-known quadratic Lyapunov function as a platform to derive stability analysis and control design conditions. However, stability and stabilization conditions based on quadratic Lyapunov function are mainly conservative. This paper presents a line-integral fuzzy Lyapunov function based stability conditions for polynomial fuzzy systems. In order to obtain more relax results, the copositive relaxation is considered. The derived conditions are expressed in terms of SOS which can be efficiently solved by using, for instance, the third-party MATLAB toolbox SOSOPT. Finally, a stability analysis example is provided to demonstrate that results obtained by copositive relaxation conditions are more relaxed than existing line-integral fuzzy Lyapunov function based approaches.