Human galectin protein 1 is one of the major carbohydrate-binding proteins and is the first member of this family which is responsible for nearly all types of cancer. Several studies have been conducted to inhibit this protein to treat cancer. However, due to the side effects of those inhibitors and also the pharmacodynamics and pharmacokinetics difficulties made these inhibitors to be less important and mostly avoided for treatment purposes. For this reason, this study was convinced to unveil the binding mechanism of two natural carbohydrate ring containing compounds, rutin and apigetrin, using computational approaches including molecular docking, binding energy calculation and ADME analysis. According to the results, it was found that the residues, Val31, Ser29, Arg48, His44, Asn33, Glu71, Asn61 and Asp123 were involved in the interactions with the CRD domain of galectin-1. Apigetrin showed higher binding free energy than rutin in MM-GBSA binding energy calculation. ADME analysis revealed that, apigetrin showed better result than rutin for maximum parameters of ADME analysis. Taken together, apigetrin can be subjected for further analysis for the development of new inhibitor against human galectin-1 protein by in vitro and in vivo experiments.