Proportional fairness (PF) is a concept widely studied in the literature, particularly in the fields of telecommunications, network design, resource allocation, and social choice. It aims to distribute utilities in a way that ensures fairness and equity among users while optimizing system performance. Under convexity, PF is equivalent to the Nash bargaining solution, a well-known notion from cooperative game theory and it can be obtained by maximizing the product of the utilities. In contrast, when dealing with non-convex optimization, PF is not guaranteed to exist and when exists, it is also the Nash bargaining solution. Consequently, finding PF under non-convexity remains challenging since it is not equivalent to any known optimization problem. This paper deals with PF in the context of combinatorial optimization where the feasible set is discrete, finite, and non-convex. For this purpose, we consider a general Max-Max Bi-Objective Combinatorial Optimization (Max-Max BOCO) problem where its two objectives to be simultaneously maximized take only positive values. Then, we seek to find the solution to achieving PF between two objectives which is referred to as proportional fair solution (PF solution). We first show that the PF solution, when exists, can be obtained by maximizing a suitable linear combination of two objectives. Subsequently, our main contribution lies in presenting an exact algorithm that converges within a logarithmic number of iterations to determine the PF solution. Finally, we provide computational results conducted on the bi-objective spanning tree problem which is a specific example of Max-Max BOCO.