Protein-peptide interactions play a key role in biological processes. Understanding the interactions that occur within a receptor-peptide complex can help in discovering and altering their biological functions. Various computational methods for modeling the structures of receptor-peptide complexes have been developed. Recently, accurate structure prediction enabled by deep learning methods has significantly advanced the field of structural biology. AlphaFold (AF) is among the top-performing structure prediction methods and has highly accurate structure modeling performance on single-chain targets. Shortly after the release of AlphaFold, AlphaFold-Multimer (AFM) was developed in a similar fashion as AF for prediction of protein complex structures. AFM has achieved competitive performance in modeling protein-peptide interactions compared to previous computational methods; however, still further improvement is needed. Here, we present DistPepFold, which improves protein-peptide complex docking using an AFM-based architecture through a privileged knowledge distillation approach. DistPepFold leverages a teacher model that uses native interaction information during training and transfers its knowledge to a student model through a teacher-student distillation process. We evaluated DistPepFold's docking performance on two protein-peptide complex datasets and showed that DistPepFold outperforms AFM. Furthermore, we demonstrate that the student model was able to learn from the teacher model to make structural improvements based on AFM predictions.