Despite the recent improvement achieved in cancer treatment strategies during the last three decades resulting in increasing the survival rate and better quality of life for cancer patients, cancer remains incurable in most cases. Search for new anti-cancer drugs is the subject of intensive research of many pharmaceutical companies and research centers. Molecular modeling simulation techniques are considered among the most modern methods to search for new drugs. In this research we decided to use molecular modeling and simulation of some derivatives 4, 6,7-trisubstituted Quinazolinones, known for their biological activities in various pharmacological uses especially as anti-tumor agents. The main idea in this work is to build a library of 90 compounds from 4,6,7-trisubstituted quinazoline family, and screen their binding affinity toward Epidermal Growth Factor (EGFR). The tested compounds are ranked according to their binding energy ΔG. The highest binding 10 compounds are analyzed in attempt to estimate their EGFR binding affinity using Molsoft ICM-Pro 3.5-0a software. The results reveled that most of the tested compounds have moderate to strong binding energy values in Kcal\mol towards EGFR target enzyme, which make them potential targets for drug discovery as new Tyrosine kinase EGFR inhibitors.