By means of first-principles calculations based on density functional theory (DFT) and hybrid functional, we studied the structural, electronic, and ferroelectric properties of the two recently synthesized high-pressure perovskite-type (orthorhombic, space group Pnma) and LiNbO3-type (rhombohedral, space group R3c) polymorphs of CdPbO3. Besides providing structural and electronic results in good agreement with available experiments, our results are able to correctly describe the pressure-induced Pnma -> R3c structural phase transition and most importantly predict the realization of proper ferroelectric behavior in LiNbO3-type CdPbO3 with an electric polarization of 52.3 mu C/cm(2). The proper covalent interaction mechanism driving the ferroelectric transition is discussed and explained in terms of the analysis of Born effective charges, potential-energy surfaces, charge density isosurfaces, and electric localization function.