The electrical conductance of two kinds of graphene nanoflakes (GNFs) is studied numerically, using non equilibrium Green's function. We perform the calculations on bowtie and rhombus GNFs within the nearest neighbor tight binding model. Our findings reveal the sensitivity of conductance on the orientation of zigzag edges. The results show that the conductance of the bowtie and rhombus GNFs could be tuned via enlarging the system size. Moreover, we obtain different results for conductance of the mentioned GNFs and rectangle zigzag GNF with the same size. (C) 2017 Elsevier B.V. All rights reserved.