A class of mini-max optimization problems is frequently encountered in machine learning. A large number of optimization algorithms have been designed for mini-max problems based on the gradient and Hessian matrix information of the objective function. However, in some applications, the gradient and Hessian matrix information are possibly computationally expensive or difficult to obtain. Therefore, under the framework of mini-max cubic Newton algorithm (MCN), a zeroth-order mini-max cubic regularized Newton algorithm (ZO-MCN) is proposed for solving the non-convex strongly concave mini-max problem by using Gaussian smoothing method to approximate the gradient and Hessian matrix based on Stein identity.The convergence and iteration complexity of the proposed algorithm are analyzed. The iteration complexity of the algorithm is the order of O（ε-3/2） for achieving a second-order stable point, where ε is the accuracy. The results of numerical simulations show that: under the same accuracy, the proposed algorithm is better than the algorithm MCN in CPU running time.