Natural convection flows in a cubical air-filled slanted cavity that has one pair of opposing faces isothermal at different temperatures, $T_h;and;T_c$, respectively, the remaining four faces having a linear variation from $T_c;toT_h$ are numerically simulated by a solution code (PowerCFD) using unstructured cell-centered method. Special attention is paid to three-dimensional flow and thermal characteristics according to a new orientation (diamond type) for the cubical-cavity benchmark problem in natural convection. Comparisons of the average Nusselt number at the cold face are made with experimental benchmark solutions found in the literature. It is found that the code is capable of producing accurately the nature of the laminar convection in a cubical air-filled slanted cavity with differentially heated walls.