Advance-retreat method is a one-dimension searching algorithm of the optimal theory and a method for single peak function, which is very simple and in common use. The main work of this paper aims at the problem of convergence and convergent speed stated as follows. Firstly, the theory and process of advance-retreat method is discussed. Secondly, an improved advance-retreat method is proposed for conquering the drawback that the original method is not convergent at some conditions. By the improved method, the alternative step changes to a function of forehead step and iterative time. Thirdly, by a strict theoretical derivation the correctness of the method is proved. Fourthly, the effectiveness of the method is verified by simulation results. Finally, the results show that the convergence speed of the advance-retreat method is changeable with the different initial parameters and by using the improved advance-retreat method, the convergence is guaranteed at any case at the cost of decreasing the convergence speed.