As promising TBC (thermal barrier coating) candidates, perovskite oxides own designable properties for their various options of cations and structural diversity, but limited comprehensions of structure-property relationship delay their engineering applications. In this work, mechanical/thermal properties of ABO(3) (A=Sr, Ba; B=Ti, Zr, Hf) perovskites and their anisotropic nature are predicted employing density functional theory. Their theoretical minimum thermal conductivities range from 1.09 to 1.74Wm(-1)K(-1), being lower than Y2O3 partially stabilized ZrO2. Reduced thermal conductivities up to 16% along particular directions are reached after considering thermal conductivity anisotropy. All compounds own high hardness while SrZrO3, SrHfO3, and BaHfO3 possess well damage tolerance. We found that small electronegativity discrepancy leads to big anisotropy of chemical bond, Young's/shear moduli and thermal conductivities, together with good damage tolerance. These results suggest that the next generation TBCs with extra low thermal conductivity should be achieved through combining material design and orientation-growth tailoring.