This paper presents a novel adaptive sub-optimal control method for continuous-time nonlinear polynomial systems from a perspective of adaptive dynamic programming (ADP). This is achieved by relaxing the problem of solving an Hamilton-Jacobi-Bellman (HJB) equation into an optimization problem, which is solved via a new policy iteration method. The proposed methodology distinguishes from previously known nonlinear ADP methods in that the neural network approximation is avoided and that the resultant control policy is globally stabilizing, instead of semiglobally or locally stabilizing. Furthermore, in the absence of the a prior knowledge of the system dynamics, an online learning method is devised to implement the proposed policy iteration technique by generalizing the current ADP theory. Finally, the proposed method is applied to a jet engine surge control problem.