In this study, we consider non-smooth finite minimax problems. A new approach for solving minimax problems is developed, employing indicator functions and smoothing functions. First, the formulation of minimax problems is revised using indicator functions. Then, a new generation smoothing technique is used for the revised formulation. An algorithm is developed to solve the revised and smoothed problems numerically. The efficiency of the algorithm is demonstrated on several test problems, and a comparison is conducted between the numerical results achieved and those of alternative approaches. Finally, the portfolio planning problem is considered as a real-life application, and satisfactory results are obtained.