Protein-peptide interactions are often associated with large-scale conformational changes that are difficult to study either by classical molecular modeling or by experiment. Recently, we have developed the CABS-dock method for flexible protein-peptide docking that enables large-scale rearrangements of the protein chain. In this study, we use CABS-dock to investigate the binding of the p53-MDM2 complex, an element of the cell cycle regulation system crucial for anti-cancer drug design. Experimental data suggest that p53-MDM2 binding is affected by significant rearrangements of a lid region - the N-terminal highly flexible MDM2 fragment; however, the details are not clear. The large size of the highly flexible MDM2 fragments makes p53-MDM2 intractable for exhaustive binding dynamics studies using atomistic models. We performed extensive dynamics simulations using the CABS-dock method, including large-scale structural rearrangements of MDM2 flexible regions. Without a priori knowledge of the p53 peptide structure or its binding site, we obtained near-native models of the p53-MDM2 complex. The simulation results match well the experimental data and provide new insights into the possible role of the lid fragment in p53 binding. The presented case study demonstrates that CABS-dock methodology opens up new opportunities for protein-peptide docking with large-scale changes of the protein receptor structure.