Epitaxial Ba0.15Zr0.85TiO3 (BZT) ferroelectric thin films with (001), (011), and (111) orientations were, respectively, grown on La0.67Sr0.33MnO3 (LSMO) buffered LaAlO3 substrates by pulsed laser deposition method. The dc electric-field dependence of permittivity and dielectric loss of (001)-, (011)-, and (111)-oriented BZT/LSMO heterostructures obeys the Johnson formula, and the ac electric-field dependence of that obeys the Rayleigh law under the subswitching field region. The anisotropic dielectric properties are attributed to the higher mobility of the charge carriers, the concentration of mobile interfacial domain walls, and boundaries in the (111)-oriental films than in the (110)- and (100)-oriented films.