In this paper, the dynamic power allocation problem over the multiple-access channel (MAC) against overhearing of eavesdroppers is investigated with the objective to maximize the users' secrecy rate under transmitted power constraints. Lyapunov drift approach is applied to derive the sub-optimal solution for this inherent non-convex optimization problem. Convergence condition and performance of the developed algorithm are investigated. Simulation results indicate that it outperforms the difference- of-two-convex-functions (DC) programming with much less computation time, and its achieved secrecy rate is close to the global optimum solution.