Ferroelectric and magnetoresistance heterostructure ͑Ba, Sr͒TiO 3 / ͑La, Sr͒MnO 3 ͑BST/LSMO͒ heterostructure is deposited epitaxially on SrTiO 3 ͑001͒ substrate by pulse laser deposition. The phase structures of the BST/LSMO heterostructure are characterized by x-ray diffraction. Cross-sectional transmission electron microscope shows a substantial interdiffusision between BST and LSMO layers. The dielectric properties and conductivity of BST/LSMO heterostructure is measured as a function of temperature, frequency, and electric field. The dielectric constant dependence on electric field, vs E, exhibits a strong nonlinear behavior in the temperature from 20 to 300 K, while ͑E=0͒ vs T relation shows a dielectric relaxor characteristic. Furthermore, the dielectric constant ͑E =0 kV/cm͒ and the dielectric tunability ͑E = 200 kV/ cm͒ are found to be similar temperature dependencies. Last, in the temperature regime where a semiconduction-type conduction became dominate, the activation thermal energy of BST/LSMO heterostructure is estimated to be 0.67 and 0.73 eV at 1 kHz and 1 MHz, respectively.