The electronic transport properties of carbohelicenes and heterohelicenes absorbed between two metal electrodes have been investigated by using the nonequilibrium Green's function in combination with the density function theory. The transport properties of the molecular junctions are mainly dependent on the nature of spiral molecules. The detailed analyses of the transmission spectra, the energy levels as well as the spatial distribution of molecular projected self-consistent Hamiltonian explain how the geometry of molecules affects the intra-molecular electronic coupling. The spiral current in the configurations can be achieved by tuning the outer edge states of spiral-shaped molecules. Furthermore, the symmetric current–voltage characteristics are investigated with the bias changing for all devices as well as an negative differential resistance behavior is observed.