Excitation energy migration and subsequent energy transfer to excimer-forming sites occurring in a quasi-two-dimensional plane of poly(isobutyl methacrylate) Langmuir-Blodgett films were investigated through the time-resolved analyses of anthracene fluorescence. Fluorescence anisotropy decays showed that the energy migration occurred more efficiently as the anthracene fraction increased. A further increase of the anthracene gave rise to the excimer-forming sites acting as energy traps, and finally the anthracene fluorescence was markedly quenched from the energy transfer to the traps. The migration process was quantitatively analyzed by a computer simulation based on the Monte Carlo method, which allowed estimation of the number of hopping and the mean-square displacement of excitons. The initial growth of the mean-square displacement with time became gradually gentle, while the number of hopping linearly increased with time. This result shows that the excitons are not diffusive and tend to stay within a small cluster of chromophores, especially for small chromophore density at short times.