An energy and exergy thermodynamic analysis using EES program was done for a domestic refrigerator working with R-134a using vapor compression refrigeration cycle. The analysis deals with the system component, i.e. compressor, condenser, evaporator and the expansion device. The analysis depends on the entropy generation minimization approach to improve the refrigerator performance by exploring the optimum design points. These design points were derived from three different theories governing the entropy generation minimization using exergy analyzing method. These theories were first applied to find the optimum balance between the hot inner condenser area and the cold inner evaporator area of the refrigerator and between its hot and cold thermal conductances. Nine types of condensers were used according to its internal surface area and thermal conductance, in order to reach the minimum entropy generation in the refrigerator. The results showed that the compressor has the lowest exergy efficiency of 25%. The expansion device was the second component after the compressor with exergy efficiency of 92%, followed by the condenser with an efficiency of 93%. The evaporator was found to have an exergy efficiency of 98 %. The experimental tests were repeated for the nine condensers sizes with three different ambient temperatures 25℃, 30℃ and 35℃.  The exergy analysis showed that the design of the refrigerator mainly depends on thermal conductance calculations rather than the surface inner area estimation.