Concerning the fairness problem of multiple Device-to-Device (D2D) users reusing the spectrum resources allocated to cellular subscribers, a power allocation algorithm based on max-min fairness was proposed under the premise of guaranteeing the rate of cellular users. First, the nonconvex optimization problem was transformed into a Difference between Convex functions (DC) programming problem, then the global optimization algorithm of convex approximation and the bisection algorithm were used to achieve power optimization of D2D. Simulation results show that compared with the global optimization algorithm which only uses convex approximation, the proposed algorithm has better convergence and maximizes the bottleneck rate of D2D users.