Heat Exchanger Network (HEN) optimization by mathematical programming has been developed for half of century. Stage-wise superstructure by Yee and Grossmann (1990) is one of the most popular HEN design models dividing process temperature into stages under assumption of constant specific heat capacity (Cp). To make model more realistic, the model is developed under temperature-dependent Cp which is a cubic equation of temperature. To simplify this circumstance, non-linearity of Cp is linearized by applying partitions of linear equations of Cp at different temperature intervals. HEN from the modified stage-wise superstructure model with variable Cp by GAMS software version 24.2 is validated with crude preheat train case from commercial simulation program (Pro/II software version 9.1). The Cp from Pro/II software as a function of temperature is divided into three linear equations of Cp at three temperature intervals. A case study of crude preheat train without HEN consists of five hot product streams and one cold crude oil stream, consuming hot and cold utilities of 175,353.53 kW and 107,945.89 kW, respectively. The new model synthesizes HEN for the crude preheat train, consuming less hot and cold utilities of 82,100.93 kW and 14,654.38 kW. The synthesized HEN is validated by Pro/II software, giving duties of hot and cold utilities of 81,835.30 kW and 14,417.20 kW. Percent error of hot and cold utilities of HEN from GAMS model are only 0.31 % and 1.65 %, compared to ones from Pro/II software. Compared to Pro/II results, percent error of process HEN area and utility HEN area from new model are 1.22 % and 2.91 %, respectively. New model with variable Cp assumption gives a good agreement with validated HEN by Pro/II. Compared to examples from other publications, the model shows that it generates HEN design with less TAC and less computational time.