A series of triazole-substituted quinazoline hybrid compounds were designed and synthesized for anticancer activity targeting epidermal growth factor receptor (EGFR) tyrosine kinase. Most of the compounds showed moderate to good antiproliferative activity against four cancer cell lines (HepG2, HCT116, MCF-7, and PC-3). Compound 5b showed good antiproliferative activity (IC50 = 20.71 μM) against MCF-7 cell lines. Molecular docking results showed that compound 5b formed hydrogen bond with Met 769 and Lys 721 and π–sulfur interaction with Met 742 of EGFR tyrosine kinase (PDB ID: 1M17). Compound 5b decreases the expression of EGFR and p-EGFR. It also induces apoptosis through reactive oxygen species generation, followed by the change in mitochondrial membrane potential.