The inelastic electron scattering properties of the molecular devices of curved finite-sized graphene nanoribbon (GNR) slices have been studied by combining the density functional theory and Green's function method. Based on the extended molecular models, the inelastic electron tunneling spectroscopy, inelastic quantum conductance and inelastic current have been calculated systematically. The temperature dependences of the inelastic electron tunneling spectroscopy (IETS) and inelastic current have been discussed. Results show that the contributions of the inelastic conductance increase obviously and become comparable to the elastic conductance for curved GNR slices based junctions. The electron inelastic scattering of the curved GNR-based junctions are orders of magnitude stronger than that of the plane ones. The obvious dependences of the elastic and inelastic current of the finite-sized GNR slices make it have probable applications in molecular microprobes.