This paper is concerned about the nonlinear optimization problem of nonzero-sum (NZS) games with unknown drift dynamics. The data-based integral reinforcement learning (IRL) method is proposed to approximate the Nash equilibrium of NZS games iteratively. Furthermore, we prove that the data-based IRL method is equivalent to the model-based policy iteration algorithm, which guarantees the convergence of the proposed method. For the implementation purpose, a singl-ecritic neural network structure for the NZS games is given. To enhance the application capability of the data-based IRL method, we design the updating laws of critic weights based on the offline and online iterative learning methods, respectively. Note that the experience replay technique is introduced in the online iterative learning, which can improve the convergence rate of critic weights during the learning process. The uniform ultimate boundedness of the critic weights are guaranteed using the Lyapunov method. Finally, the numerical results demonstrate the effectiveness of the data-based M. algorithm for nonlinear NZS games with unknown drift dynamics.