The authors report the epitaxial growth and the dielectric properties of relaxor ferroelectric 0.5Ba(Zr0.2Ti0.8)O3–0.5(Ba0.7Ca0.3)TiO3 thin films with atomically flat surface on GdScO3 single crystal substrates. The authors studied the effects of growth conditions, such as the substrate temperature and the oxygen pressure on the structure of the thin films, as measured by x-ray diffraction, to identify the optimal growth conditions. The authors achieved sustained layer-by-layer growth of 0.5Ba(Zr0.2Ti0.8)O3–0.5(Ba0.7Ca0.3)TiO3 films as monitored by in situ and real time reflective high energy electron diffraction. Atomic force microscopy investigations showed atomically smooth step terrace structures. Aberration-corrected scanning transmission electron microscopy images show good epitaxial relation of the film and the substrate without any line defects. High dielectric constant (∼1400) and slim hysteresis loops in polarization-electric field characteristics were observed in 0.5Ba(Zr0.2Ti0.8)O3–0.5(Ba0.7Ca0.3)TiO3 films, which are characteristic of relaxor-type ferroelectric materials.