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A first principles study with density functional theory method has carried for parallelogram graphene nanoflakes. In this work, we used ABINIT package to calculate the fundamental properties of parallelogram graphene nanoflakes in armchair and zigzag types, due to the increase of the number of atoms. The effect of defect for these characters in each type is also presented. Depend on the calculation results, the bandgap of parallelogram graphene nanoflakes only exists in armchair types with largest bandgap 0.021 eV for 54 atoms, while the zigzag types have no bandgap. Based on these results, it can be said that the properties of parallelogram graphene nanoflakes is semimetal. In addition, the density of states results shows that the magnetic properties of parallelogram graphene nanoflakes is non-magnetic since the symmetrical properties between density of states in spin up and spin down. Based on the results study of defect effect, it was found that the defect only affected the bandgap, but not the magnetic properties.