Binding of tyrosine (Tyr) with two finite size graphene sheets of 62 and 186 carbon atoms was investigated using M06-2X/6-31G(d) level. Thorough conformational analysis was done for tyrosine to select few conformers to explore their complexation by considering different orientations on the surface of graphene. The binding energy values are not significantly changed while moving from small to large graphene. Tyrosine exhibits strong pi-pi interactions that support recent experiments on binding of aromatic amino acids on the surface of graphene and modified graphene. The binding energies of 9.4-9.9 kcal/mol were obtained for different conformers of tyrosine binding with graphene via parallel orientation (having pi-pi and C(beta)-H ... pi interactions). Owing to multiple interactions including C-H ... pi, N-H/O-H ... pi and pi-pi, the bent prefers over parallel orientation (by 1 kcal/mol) for the high energy conformer of Tyr adsorption on graphene. The binding energies in the aqueous medium are slightly lower than those obtained in the gas phase. HOMO-LUMO energy gaps calculated at the TPSSh/6-31G(d) level suggest that adsorption of tyrosine conformers with different orientations on the surface of graphene does not affect the band gap value of graphene (1.43 and 0.08 eV correspondingly for small and large graphene). Intermolecular orbital interactions support the pi-pi interactions in bent and parallel orientations of tyrosine with graphene.