Graphene-based nanomolecular devices are formed by connecting one of the prototype molecular materials of graphene nanoribbons to two Au electrodes. The geometric structure and electronic properties are calculated by using density functional theory. Basing on the optimized structure and the electronic distributions, we obtain the transport properties of the devices by using the Green's functional method. It is found that that the geometry structures of the molecule and the transport properties are sensitive to the distance between source and drain electrodes. With increasing the distances, the curvature radius of the atomic plane is increased, and the deformation energy is decreased. The current versus voltage curves have almost same threshold voltage with different distances between the electrodes. The transmission probability, the density of states and the external bias voltage play important role in determining the transport properties of the molecular devices.