Structure of penetrable sphere fluids, which are generally used to model micelles in a solvent or star polymer solutions, has been studied by integral equation theory with a very simple closure relation based on a modification of the Verlet-modified bridge function, which has been known to be very successful for hard body fluids. Conventional integral equation theories, which use Percus-Yevick and hypernetted chain closures, are unable to correctly model the behavior of the pair distribution functions of the penetrable sphere fluids, particularly in the core overlap region. The results for the pair-distribution or radial distribution functions obtained from the present theory are found to be in excellent agreement with the corresponding computer simulation results. The bridge functions at various temperatures and densities have also been compared with the corresponding results extracted from the computer simulation. (C) 2003 American Institute of Physics.