Disordered protein-protein interactions (PPIs), those involving a folded protein and an intrinsically disordered protein (IDP), are prevalent in the cell, including important signaling and regulatory pathways. IDPs do not adopt a single dominant structure in isolation but often become ordered upon binding. To aid understanding of the molecular mechanisms of disordered PPIs, it is crucial to obtain the tertiary structure of the PPIs. However, experimental methods have difficulty in solving disordered PPIs and existing protein-protein and protein-peptide docking methods are not able to model them. Here we present a novel computational method, IDP-LZerD, which models the conformation of a disordered PPI by considering the biophysical binding mechanism of an IDP to a structured protein, whereby a local segment of the IDP initiates the interaction and subsequently the remaining IDP regions explore and coalesce around the initial binding site. On a dataset of 22 disordered PPIs with IDPs up to 69 amino acids, successful predictions were made for 21 bound and 18 unbound receptors. The successful modeling provides additional support for biophysical principles. Moreover, the new technique significantly expands the capability of protein structure modeling and provides crucial insights into the molecular mechanisms of disordered PPIs.