We studied the noncovalent interactions of yttrium bisphthalocyanine YPc2 with graphene sheet models with and without topological defects. The density functional theory results obtained for the cluster models containing Stone-Wales defect (SW), isolated pentagon (5) and pyracylene unit (5665) were compared to those for defect-free graphene sheet (G). The optimized geometry for adsorption complexes, bonding strength and some electronic parameters were analyzed. In all cases YPc2 molecule suffers considerable distortion, whose direction and degree depend on a particular model and site of adsorption (‘exo’ and ‘endo’, in the case of conical 5 and 5665 models); also, it is more pronounced for Pc ligand directly contacting graphene surface. In the case of 5_exo and 5665_exo complexes, the bending follows the direction of already existing curvature of Pc ligand, whereas for 5_endo and 5665_endo its direction changed. For G and SW models, the changes in curvature result in almost flat geometry of contacting Pc. The interactions are strong for all the noncovalent complexes analyzed, increasing in the following order: 5665_endo <5665_exo < 5_exo < 5_endo < G < SW. The plots of HOMO, LUMO and spin density are analyzed, as well as the changes in HOMO-LUMO gap energy.