From a quantum information point of view, preparation and control of the atomic optimal entropy squeezing state(AOEST) are researched for the system of a moving two-level atom entanglement with the field under the intensity-dependent coupling. Its results with those of atomic squeezing based on the Hesienbeg uncertainty relation is compared; sufficient and necessary conditions of preparation of the AOEST is analyzed and numerical verification of the AOEST is done. The influence of the field-mode structure parameter on the AOEST is examined. It is shown that information entropy squeezing is a remarkable precision measure for the atomic squeezing. The AOEST can be prepared by controlling the time of the atom interacting with the field, cutting the entanglement bewteen the atom and field, choosing coherence of the atom and modulating relative phase of the systems. A lasting AOEST can be obtained by controlling the field-mode structure parameter.