This article demonstrates the synthesis of 1,2,4-triazole derivatives and their applications in medicine particularly as anti-breast cancer agents which is a major issue of the present. The synthesized compounds were characterized by elemental analysis, FT-IR and NMR. DFT was used to study the quantum chemical calculations of geometries and vibrational wave numbers of 3-hydroxynaphthyl and p-tolyl substituted 1,2,4-triazoles in the ground state. The scaled harmonic vibrational frequencies obtained from the DFT method were compared with those of the FT-IR spectra and found good agreement. The synthesized 1,2,4-triazole-naphthyl hybrids were screened for the anticancer activity against MCF-7 breast cancer lines. Among them compounds 3 and 7 showed broad spectrum anticancer activity with IC 50 values 9.7 μM and 7.10 μM, respectively and their activity is comparable to that of the standard drugs. The molecular model for binding between the compounds (1-8) and the active site of BRCA2 was obtained on the basis of the computational docking results and the structure-activity relationship.