Inhibiting of Proprotein Convertase Subtilisin/Kexin-type 9 (PCSK9) and Low Density Lipoprotein Receptor (LDLR) binding is an effective way for reducing Low Density Lipoprotein cholesterol (LDL-C). Understanding the interaction between PCSK9 and LDLR is useful for PCSK9 inhibitor design. In this work, MD simulations with the standard (non-polarizable) AMBER force field and effective polarizable bond (EPB) force field were performed for wild type and four mutants of PCSK9 and EGFA (Epidermal Growth Factor-like repeat A) domain of LDLR complexes. These four mutants are gain-of-function mutants. The analysis of hydrogen bond dynamics and the relative binding free energy indicates that EPB is more reliable in simulating protein dynamics and predicting relative binding affinity. Structures sampled from MD simulations with the standard AMBER force field deviate too far away from crystal structures. Many important interaction components between of PCSK9 and EGFA no longer exist in the simulation with the Amber force field. For comparison, simulation using EPB force field gives more stable structures as shown by hydrogen bond analysis and produced relative binding free energies that are consistent with experimental results. Our study suggests that inclusion of polarization effects in MD simulation is important for studying the protein-protein interaction.