We investigated the structural, elastic, and electronic properties of the cubic perovskite-type BaHfO3 using a first-principles method based on the plane-wave basis set. Analysis of the band structure shows that perovskite-type BaHfO3 is a wide gap indirect semiconductor. The band-gap is predicted to be 3.94 eV within the screened exchange local density approximation (sX-LDA). The calculated equilibrium lattice constant of this compound is in good agreement with the available experimental and theoretical data reported in the literatures. The independent elastic constants (C11, C12, and C44), bulk modules B and its pressure derivatives B^′, compressibility β, shear modulus G, Young's modulus Y, Poisson's ratio ν, and Lame´ constants (μ, λ) are obtained and analyzed in comparison with the available theoretical and experimental data for both the singlecrystalline and polycrystalline BaHfO3. The bonding-charge density calculation make it clear that the covalent bonds exist between the Hf and O atoms and the ionic bonds exist between the Ba atoms and HfO3 ionic groups in BaHfO3.