Discrete ordinates interpolation method (DOIM) developed for the numerical solution of the radiative transfer equation (RTE) is further developed to unstructured grid systems in arbitrary three-dimensional geometries. It is applied to several problems with absorbing, emitting and non-scattering medium. In this study, commercial grid generation program is used to make a grid of complicated geometries easily. Locating interpolation surface, new interpolation methods and method of treating boundaries are suggested to apply to arbitrary three-dimensional geometry. Three simple grid systems in given temperature field or radiative equilibrium with unknown temperature field are considered to validate the locating interpolation surface and the method of treating boundaries. The wall heat flux is calculated and compared with the exact solution or a reference value. The results of DOIM are in good agreement for arbitrary three-dimensional enclosures. And DOIM is also applied to complicated geometry of power plant boiler. The result is compared with the wall heat flux obtained by $REM^2$ method. Similar results are found between them.