This study proposes a new numerical analysis method for assessing the outage cost of the composite power system with considering transmission system at load points. The proposed method comes from combination of the expected energy not served curve(EENSC) with the marginal outage cost function obtained at load points. Uncertainty of the outages of the generation and transmission systems was also included in this study. This study can be categorized into three processing parts as like as follows. Firstly, EENSC at load points was developed newly from the composite power system effective load duration curve which has been proposed by the authors. Secondly, this study proposes a new technical method for determining the coefficients of the marginal outage cost functions at load points in the composite power system(Generation and Transmission systems). It is a main key point that the mathematical expression for the marginal outage cost function at a load point is formulated and evaluated using relations between the GNP (or GDP) and the electrical energy demand at the load pint. Finally, the outage cost was calculated in this paper by combining the proposed EENSC with the marginal outage cost function evaluated at each load point. It is another important feature that the average costs for future at load points can be forescasted using the proposed approach. The effectiveness of the proposed new approach is demonstrated by the case studies with the IEEE-RTS.