In this paper, we propose an identifier-critic-based approximate dynamic programming (ADP) structure to online solve H infinity control problem of nonlinear continuous-time systems without knowing precise system dynamics, where the actor neural network (NN) that has been widely used in the standard ADP learning structure is avoided. We first use an identifier NN to approximate the completely unknown nonlinear system dynamics and disturbances. Then, another critic NN is proposed to approximate the solution of the induced optimal equation. The H infinity control pair is obtained by using the proposed identifier-critic ADP structure. A recently developed adaptation algorithm is used to online directly estimate the unknown NN weights simultaneously, where the convergence to the optimal solution can be rigorously guaranteed, and the stability of the closed-loop system is analysed. Thus, this new ADP scheme can improve the computational efficiency of H infinity control implementation. Finally, simulation results confirm the effectiveness of the proposed methods.