Rubidium magnesium monophosphate (RbMgPO4) compound was prepared from highly pure constituents by solid state reaction. It was characterized by X-ray powder diffraction, IR, Raman, differential scanning calorimetry (DSC) and impedance spectroscopy. The infrared and Raman spectra were interpreted on the basis of O-4(3-) vibrations. DSC revealed two displacive and reversible phase transitions at T-1 = 442/432 K and T-2 = 460/445 K (heating/cooling). The electrical conductivity was measured in the frequency and temperature range 200 Hz-5 MHz and 423 K-523 K, respectively. The obtained results were analysed by fitting the experimental data to an equivalent circuit model. The temperature dependence of alternating and direct current conductivities (sigma(ac), sigma(dc)) confirms the observed transitions in the calorimetric study; they were described in terms of Arrhenius relation. The activation energy's values were determined in each phase. The AC conductivity behavior is ensured by a single process defined as a hopping transport mechanism. The conductivity frequency dependence was interpreted using the correlated barrier-hopping model (CBH) in all phases.