In recent years, chalcones and their derivatives have become the focus of global scientists due to increasing evidence reported towards their potency in antitumor and anti-cancer. Here, the chalcones designed and synthesized in our present study were derived from the derivatives of naphthaldehyde and acetophenone. Both these precursors have been reported in demonstrating a certain degree of anticancer property. Also, the substituents on these precursors such as hydroxyl, methoxy, prenyl, and chloro were shown able to enhance the anticancer efficiency. Hence, it is the interest of the current study to investigate the anticancer potential of the hybrid molecules (chalcones) consisting of these precursors with different alkoxy substituents and with or without the fluorine moiety. Two series of chalcone derivatives were designed, synthesized, and characterized using the elemental analysis, IR, 1 H and 13 C NMR spectroscopy, subsequently evaluated for their anti-cancer activity. Interestingly, the results showed that the fluorinated chalcones 11-15 exhibited stronger cytotoxic activity towards the breast cancer cell lines (4T1) compared to non-fluorinated chalcone derivatives. Remarkably, the selectivity index obtained for these fluorinated chalcones derivatives against the breast cancer 4T1 cell line was higher than those exhibited by cisplatin, which is one of the most frequently deployed chemotherapy agents in current medical practice. These findings could provide an insight towards the potential of fluorinated chalcones being developed as an anti-cancer agent with moderate activity towards breast cancer cell and low inhibition of fibroblast cell at a concentration of 100 μM.