Sum of squares (SOS) polynomials have provided acomputationally tractable way to deal with inequality constraintsappearing in many control problems. It can also act as an approx-imator in the framework of adaptive dynamic programming. Inthis paper, an approximate solution to theH∞optimal control ofpolynomial nonlinear systems is proposed. Under a given attenu-ation coefficient, the Hamilton–Jacobi–Isaacs equation is relaxedto an optimization problem with a set of inequalities. After apply-ing  the  policy  iteration  technique  and  constraining  inequalitiesto  SOS,  the  optimization  problem  is  divided  into  a  sequenceof  feasible  semidefinite  programming  problems.  With  the  con-verged  solution,  the  attenuation  coefficient  is  further  minimizedto  a  lower  value.  After  iterations,  approximate  solutions  to  thesmallestL2-gain  and  the  associatedH∞optimal  controller  areobtained. Four examples are employed to verify the effectivenessof the  proposed  algorithm.