We report a theoretical study on spin-polarized lateral displacement for the electron across a magnetic nanostructure with a zero average magnetic field, which can be experimentally realized by depositing a ferromagnetic stripe with a plumb magnetization on the top of a semiconductor heterostructure. It is shown that, the lateral displacement depends strongly on the electron spins due to the Zeeman coupling and the intrinsic symmetry, though the average magnetic field is vanishing in the nanostructure. It is also shown that the spin-polarized lateral displacement is related closely to the structural parameters. Therefore, such a novel magnetic nanostructure may be used as a spin spatial splitter for spintronics applications. (C) 2014 Elsevier B.V. All rights reserved.