Multiferroic hybrid structures PbZr0.2Ti0.8O3 (PZT)/La0.7Sr0.3MnO3 (LSMO) and PZT/MgO/LSMO were epitaxially deposited on (001) Nb:SrTiO3 crystals. Crystallinity and ferroelectric domain structures were investigated for the PZT/LSMO heterostructure. Interestingly, relatively high non-volatile magnetoelectric coupling effects were observed in both heterostructures at room temperature. The change of chemical valence for Mn and Ti at the PZT/MgO/LSMO interface may play a dominant role rather than external strain or orbital reconstruction, which lead to a large modulation of the magnetization. Correspondingly, the transport behavior of the PZT/MgO/LSMO heterostructure is investigated to confirm the role of oxygen vacancies motion. Our result indicates that the PZT/MgO/LSMO heterostructure have a promising application for future high-density non-volatile memories.