Preparation of a lead-free system (Ba0.8Ca0.2)TiO3-xBi(Mg0.5Ti0.5)O3 (BCT-BMT) with x = 0, 0.1, 0.2, 0.3, 0.4, and 0.5 was carried out using a solid-state reaction technique. X-ray (XRD) diffraction analysis confirmed a tetragonal structure for x = 0, which shifted to cubic (pseudocubic) at x ≥ 0.1. From Rietveld refinement, a single phase with a tetragonal symmetry model (P4mm) was observed for x = 0, and however, for sample x = 0.1 and sample x = 0.5, the data are modeled to cubic (Pm3m). Composition x = 0 showed a prominent Curie peak, typical of ordinary ferroelectrics with a Curie temperature (Tc) ∼130 °C, modified to a typical relaxor dielectric at x ≥ 0.1. However, samples at x = 0.2-0.5 displayed a single semicircle attributed to the bulk response of the material, whereas a slightly depressed second arc appeared for x = 0.5 at 600 °C, indicating a slight contribution to the electrical properties, ascribed to the grain boundary of the material. Finally, the dc resistivity increased with the increase of the BMT content and the solid solution increased the activation energy from 0.58 eV at x = 0 to 0.99 eV for x = 0.5. Adding the BMT content eliminated the ferroelectric behavior at compositions x ≥ 0.1 and led to a linear dielectric response and electrostrictive behavior with a maximum strain of 0.12% for x = 0.2.