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 IC50 values 9.7 mu M and 7.10 mu M, 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.