The refining industry is an energy-intensive industry; most of the energy is consumed in heating and cooling requirements. Revamping or retrofitting of existing chemical engineering plants is an appropriate opportunity for improving and enhancing the existing heat exchanger network’s (HEN) design and performance. Revamping is commonly used to modify the existing process for many objectives, such as saving energy, reducing the environmental emissions and increasing the productivity of the plant. This paper presents a new graphical approach for the analysis and revamping of existing HENs based on pinch analysis rules. The HEN is represented on a simple graph, where the cold stream temperatures are plotted on the X-axis, while the temperature driving forces for each exchanger are plotted on the Y-axis. This graphical technique describes the energy analysis problems in terms of temperature driving force (TDF) inside the heat exchanger, which is an important factor in the revamping process as the difference in that temperature driving force is involved in the calculation of the area of heat exchangers, consequently affecting the cost. Also, each exchanger is represented in this graph as a straight line whose slope is related to the heat capacities and length is related to the heat flow. The TDF graphical approach is applied to an existing HEN in an Egyptian crude oil refinery. The detailed steps for the graphical analysis and revamping are applied on the HEN for the objective of energy savings, and obtained results showed savings of approximately 10.5% in the energy demand with minor structural modifications and equivalent energy cost savings of 360,000 $/year.