Based on the minimization of the Lagrange formula, which is composed of two kinds of information measure, the maximum entropy method (MEM) is derived for diffractive imaging contaminated by quantum noise. This gives a suitable object corresponding to the maximum entropy principle with an iterative procedure. The MEM-based iterative phase retrieval algorithm with the initial process of the hybrid input-output (HIO-MEM) is presented, and a simple numerical example shows that the algorithm is effective for Poisson noise added to Fourier intensity. The relationship between the newly derived MEM for diffractive imaging and the conventional MEM for structure analysis based on crystallography is revealed.