The most common and deadly type of lung cancers around the globe was the non-small-cell lung cancer with approximately 1.5 million cases and a 5-year survival rate of less than 20%. Therefore, there is need for more active drugs to treat this problem. Molecular docking study was carried out on thirty two set of anilinopyrimidines analogues as epidermal growth factor receptor tyrosine kinase inhibitors using Molegro Virtual Docker (MVD). Ten (10) compounds with the best plant scores (binding affinities) among the compounds under investigation were reported in this study. All the ten compounds were observed to have plant score between −75.2644 to −94.2497, respectively. Their interactions in the active site of their target receptor (3IKA) were via hydrogen, hydrophobic, and electrostatic bonds sharing the following common amino acid residues LEU718, LEU844, PHE732, ALA743, VAL726, and MET793, respectively. This study also predicts the ADMET properties of these compounds under investigation and found to have good pharmacokinetic properties. It further predicts their drug-likeness properties and found to be orally bioavailable with good bioavailability scores. It concluded that these compounds could be used as potential drugs for the treatment of EGFR T790M/ L858R double mutations.