Three-dimensional heat transfer characteristics for natural convection flows are numerically investigated in the doubly-inclined cubical-cavity according to the variation of a newly defined orientation angle ?? of the hot wall surface from horizontal plane at moderate Rayleigh numbers. Numerical simulations of laminar flows are conducted in the range of Rayleigh numbers($10^4{leq}Ra{leq}10^5$) and $0^{circ}{leq}{alpha}90^{circ}$ with a solution code(PowerCFD) employing unstructured cell-centered method. Comparisons of the average Nusselt number at the cold face are made with benchmark solutions and experimental results found in the literature. It is found that the average Nusselt number at the cold wall has a maximum value around the specified orientation ${alpha}$ at each Rayleigh number. Special attention is also paid to three-dimensional thermal characteristics in natural convection according to new orientation angles at Ra??= $1{ imes}10^5$, in order to investigate a new additional heat transfer characteristic found in the range of above Ra = $6{ imes}10^4$.