In this paper, the continuous-time zero-sum game problem with asymmetric constraints is investigated by making use of the adaptive critic control approach. To begin with, a novel nonquadratic function is established to deal with the asymmetric constraint problem, which relaxes the restriction on the control matrix. Secondly, the optimal control, the worst disturbance, and the Hamilton-Jacobi-Isaacs equation are derived. After that, an adaptive critic control method is constructed to approximate the optimal cost function, so as to obtain the near-optimal control as well as the near-worst disturbance. It is worth mentioning that for the zero-sum game problem with asymmetric constraints, this paper proposes an innovative critic learning criterion to strengthen the learning process and eliminate the dependence on the initial admissible control, which has not been considered in previous papers. Moreover, the stability of the system state and the weight estimation error of the critic network is proved by using the Lyapunov method. In the end, the effectiveness of the algorithm proposed in this paper is verified by utilizing two examples, namely, the F-16 aircraft and the inverted pendulum. At the same time, for comparison, the simulation results under the traditional learning algorithm are provided to further illustrate the feasibility of the innovative learning criterion proposed in this paper.