This paper detailedly studies the transmission probability, the spin polarization and the conductance of the ballistic electron in a nanostructure with the periodic magnetic-electric barriers. These observable quantities are found to be strongly dependent not only on the magnetic configuration, the incident electron energy and the incident wave vector,but also on the number of the periodic magnetic-electric barriers. The transmission coefficient and the spin polarization show a periodic pattern with the increase of the separation between two adjacent magnetic fields, and the resonance splitting increases as the number of periods increases. Surprisingly, it is found that a polarization can be achieved by spin-dependent resonant tunnelling in this structure, although the average magnetic field of the structure is zero.