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In this data article, M06-2X/6-31G(d) level optimized geometries of complexes of tyrosine conformers binding with graphene sheets are shown in top and side views with selected non-bonding distances. The images of frontier molecular orbitals from HOMO-15 to LUMO+15 of the complexes involving graphene with tyrosine conformers are presented and the isovalue is 0.003 au. For some complexes involving small graphene, the orbitals are from HOMO-5 to LUMO+5. The molecular orbitals highlighted with frames show obvious overlaps between the fragments. Total energies of small and large graphene (GS and GL) and selected tyrosine conformers in gas and aqueous phases obtained at M06-2X/6-31G(d) level are given. The data also include total energies of all complexes in the gas phase and the aqueous phase, binding energies, BSSE (basis set superposition error) correction, and BSSE-corrected binding energies in gas phase and solvation effect on the binding energies obtained at M06-2X/6-31G(d) level. Mulliken charges of tyrosine conformers in gas and aqueous phases, and the deformation energy for tyrosine and graphene in the gas phase complexes are provided. The values of the highest occupied molecular orbital (HOMO), the lowest unoccupied molecular orbital (LUMO) and HOMO-LUMO energy gaps for some of graphene-tyrosine complexes that were not reported in the article [1] are given. The data is related to the research article “Conformation dependence of tyrosine binding on the surface of graphene: Bent prefers over parallel orientation” [1].