Design of effective cooperative jamming (CJ) algorithm is studied in this paper to maximize the achievable secrecy rate when the total transmit power of the source and multiple trusted terminals is constrained. Recently, the same problem was studied in [1] and an optimal algorithm was proposed involving a one-dimensional exhaustive searching.However, the computational complexity of such exhaustive searching could be very high, which may limit the practical use of the optimal algorithm. We propose an asymptotically optimal algorithm, involving only a fast line searching, which can guarantee to achieve the global optimality when the total transmit power goes to infinity. Numerical results demonstrate that the proposed asymptotically optimal algorithm essentially gives the same performance as the algorithm in [1, (44)] but with much lower computational complexity.