Drug-resistance is a major challenge in targeted therapy of EGFR mutated non-small cell lung cancers (NSCLCs). The third-generation irreversible inhibitors such as AZD9291, CO-1686 and WZ4002 can overcome EGFR T790M drug-resistance mutant through covalent binding through Cys 797, but ultimately lose their efficacy upon emergence of the new mutation C797S. To develop new reversible inhibitors not relying on covalent binding through Cys 797 is therefore urgently demanded. Gö6976 is a staurosporine-like reversible inhibitor targeting T790M while sparing the wild-type EGFR. In the present work, we reported the complex crystal structures of EGFR T790M/C797S + Gö6976 and T790M + Gö6976, along with enzyme kinetic data of EGFR wild-type, T790M and T790M/C797S. These data showed that the C797S mutation does not significantly alter the structure and function of the EGFR kinase, but increases the local hydrophilicity around residue 797. The complex crystal structures also elucidated the detailed binding mode of Gö6976 to EGFR and explained why this compound prefers binding to T790M mutant. These structural pharmacological data would facilitate future drug development studies.