Background: Through this study, the Chemical composition realized by UHPLC-DAD-ESI-MSn allowed the detection of different phenolic compounds groups from Pistacia atlantica Desf. leaves extracts. We studied the inhibition of main protease (CL3 Mpro) and RNA-dependent RNA polymerase (RdRp) of the SARS-CoV-2 by the identified molecules through molecular docking. Objective: The objective of this study is to identify compounds from Pistacia atlantica Desf. leaves extracts, which might have anti-viral effects. Methods: Chemical composition realized by UHPLC-DAD-ESI-MSn, the inhibition of main protease (CL3 Mpro) and RNA-dependent RNA polymerase (RdRp) of the SARS-CoV-2 is studied using molecular docking with Autodock Vina software. ADMET analysis was carried out. Results: The identified compounds are quinic acid, digallic acid, galloylquinic acid, gallic acid, trigallic acid, digalloylquinic acids, trigalloylquinic acids and methyl gallate; digallic and quinic acids are the best inhibitors. Digallic acid had binding affinity energy (BAE) of -8.2 kcal/mol, and Ki of 1µM for the CL3 Mpro, Ki of 0.62 mM for the RdRp. Quinic acid showed Ki of 4.6 mM, recorded for both enzymes. Through ADMET analysis, we have found that the two molecules are good drugs candidate. Conclusion: This is the first time that a group of identified compounds from Pistacia atlantica Desf. leaves is studied for their potential activity against the novel virus by inhibiting two key enzymes in its life cycle, and no further studies have been published in this context.