A newly designed lead-free complex ceramic with the chemical formula Ca3Bi2MoO9 has been synthesized using a conventional solid-state reaction technique. The structure, microstructure, resistive, dielectric, and conductivity characteristics have been experimentally tested. Analysis of the X-ray diffraction spectrum suggests the sample has monoclinic crystal symmetry (a = 10.639 & Aring;, b = 9.674 & Aring;, c = 6.396 & Aring;, beta= 93.794 degrees). The lattice strain and average crystallite sizes are - 0.00114 and 24.17 nm. The compactness and quality of the material have been analyzed by FESEM and EDX spectrum. The fabricated and newly designed electronic material have effective temperature and frequency-dependent electrical characteristics. The study of the conductivity of the material confirms the Universal power law. Analysis of Impedance spectroscopy data (temperature and frequency dependent) confirms that the presence of grains and grain boundaries are responsible for the resistivity properties of the material. A depressed semicircular arc (at 450 degrees C) with an angle of 2.82 degrees elaborate the non-Debye relaxation phenomena. High dielectric permittivity, minimal tangent loss, and negative temperature coefficient response are observed in the material.