We demonstrate, based on low-temperature scanning tunneling microscopy (STM) and spectroscopy, a pronounced negative differential resistance (NDR) in spin-crossover (SCO) molecular devices, where a FeII SCO molecule is deposited on surfaces. The STM measurements reveal that the NDR is robust with respect to substrate materials, temperature, and the number of SCO layers. This indicates that the NDR is intrinsically related to the electronic structure of the SCO molecule. Experimental results are supported by density functional theory (DFT) with nonequilibrium Green's function (NEGF) calculations and a generic theoretical model. While the DFT+NEGF calculations reproduce NDR for a special atomically sharp STM tip, the effect is attributed to the energy-dependent tip density of states rather than the molecule itself. We, therefore, propose a Coulomb blockade model involving three molecular orbitals with very different spatial localization as suggested by the molecular electronic structure.