Escape time algorithm is a universal algorithm when to create fractal image. A class of algorithms based on escape time algorithm is wasting-calculation. In this essay, when ombined with the feature of eventually periodic point of functions, we define a kind of points as no-escape point. To analyze the shortcomings of the classic algorithm, we improve the escape time algorithm base on the no-escape points. We analyze the algorithm and put forward the best application scope for it. By create lots of fractal figures, we find the figures created by the two algorithms are consistent with each other except a few escape points. We compare the omplexity between the two algorithms and find the iteration times by the improved algorithm are less than escape time algorithm when creating the fractal images. We do several experiments and find the improved algorithm is universal and it reduces the time-consuming.