The paper presents the results of a study of changes in the phase composition and dielectric properties of perovskite-like composites of the LiBaZrOx type depending on the temperature of the heat treatment. According to the data obtained, the initial samples obtained by the solid-state synthesis method are a three-phase system with the dominance of the orthorhombic phase ZrO2, the average nanoparticle size of which consists of composites, does not exceed 90–110 nm. As a result of thermal annealing, the dependences of phase transformations, as well as the dynamics of structural ordering with the formation of core-shell structures at an annealing temperature of 1000 °C, were established. The reduction of distortions and deformations of the crystal structure as a result of thermal annealing leads to an improvement in ferroelectric properties, as well as a decrease in the Curie temperature characteristic of the maximum dielectric constant. The weak dependence of the change in the dielectric constant with increasing frequency in the temperature range exceeding the Curie temperature indicates the relaxor nature of the properties of composites.