Lead-free (1−x)Ba(Zr0.15Ti0.85)O3–x(K0.5Na0.5)NbO3; x=0–0.05) (BZT–KNN) perovskite ceramics, a materials with potential applications for energy storage, are investigated. The samples are prepared by a solid-state reaction method. Powder X-ray diffraction (XRD) and scanning electron microscopy (SEM) are used to study the microstructure of the samples. Their dielectric properties and impedance spectra are reported as functions of temperature and frequency. The addition of 1 mol % (K0.5Na0.5)NbO3 to Ba(Zr0.15Ti0.85)O3 improves the dielectric constant and enhances its diffuseness in a wide temperature range. The small amount of (K0.5Na0.5)NbO3 is found to markedly affect the microstructure of the Ba(Zr0.15Ti0.85)O3 ceramic (grain size and other characteristics) without changing the phase or crystal symmetry. In addition, we report that fine substructures in the grains, so-called sheet structures, are responsible for the dielectric properties (both diffuseness and dielectric constant) of (1−x)Ba(Zr0.15Ti0.85)O3–x(K0.5Na0.5)NbO3 (x=0–0.03; especially x=0.01) ceramics.