To solve the problem of the best observation region fast automous prediction for lunar ultra-long wave interferometer, this article makes use of improved binary search method. During the mission period of lunar ultra-long wave interferometer, numerical solutions to relative real-time position of sun, earth, moon and the interferometer are known by the orbit prediction algorithm on board, so the prediction problem is equal to the one-dimension boundary search problem with the assumption. Frequently-used one-dimesion search methods for extremum, such as binary search, golden section search, and fibonacci search, were improved so that they could be applied to the boundary search problem. The specific improvement was to reduce search range by rough search firstly and then design new convergence criterion to find the accurate time when the interferometer gets in or out of the best observation region. Finally, search efficiency of the above methods was assessed by comparing the search time and calculation in the same precision requirement. According to the simulation results, the search time and calculation amount of the improved binary search were both slightly higher than half of those of the other methods. So improved binary search whose search efficiency is significantly better than that of the improved Fibonacci method and the golden section method can be applied to fast autonomous prediction of the best observation for lunar ultra-long wave interferometer.