The entropy squeezing of a two-level atom in motion interacting with a quantized field is investigated using quantum information entropy. The influences of the atomic motion and the field-mode structure on the atomic entropy squeezing are discussed. The numerical results obtained from the uncertainty relation of quantum information entropy are compared to those obtained from the uncertainty relation of Heisenberg. It is shown that the atomic motion leads to the periodic evolution of the entropy squeezing; an increase in field-mode structure parameter results in not only shortening of the evolution period of the entropy squeezing but also prolonging of the squeezing time; the moving atom may exhibit long time entropy squeezing effect for some choisen system parameters; the definition of variance squeezing based on the uncertainty relation of Heisenberg is trivial when atomic inversion is zero and the information entropy squeezing is a high sensitive measure for the squeezing effect of the atom.