Human Epidermal Growth Factor Receptor-1 (EGFR), a transmembrane tyrosine kinase receptor (RTK), has been associated with several types of cancer, including breast, lung, ovarian, and anal cancers. Thus, the receptor was targeted by a variety of therapeutic approaches for cancer treatments. A series of chalcone derivatives are among the most highly potent and selective inhibitors of EGFR described to date. A series of chalcone derivatives were proposed in this study to investigate the intermolecular interactions in the active site utilizing molecular docking and molecular dynamics simulations. After a careful analysis of docking results, compounds 1a and 1d were chosen for molecular dynamics simulation study. Extensive hydrogen bond analysis throughout 7 ns molecular dynamics simulation revealed the ability of compounds 1a and 1d to retain the essential interactions needed for the inhibition, especially MET 93. Finally, MM-GBSA calculations highlight on the capability of the ligands to bind strongly within the active site with binding energies of −44.04 and −56.6 kcal/mol for compounds 1a and 1d, respectively. Compound 1d showed to have a close binding energy with TAK-285 (−66.17 kcal/mol), which indicates a high chance for compound 1d to exhibit inhibitory activity, thus recommending to synthesis it to test its biological activity. It is anticipated that the findings reported here may provide very useful information for designing effective drugs for the treatment of EGFR-related cancer disease.