Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been considered as global public health security threats. Due to its rapid spread, high mortality rate and unavailability of treatment, we need to find a potent drug against SARS-CoV-2. Natural products are useful agents for the discovery of new potential drugs to combat coronavirus. Artemisia campestris, an aromatic plant widely used in traditional medicine, particularly in southern region of Algeria, is recognized for its essential oils and phenolics compounds possessing a wide range of biological activities. This study selected sixty-nine compounds from this plant to determine their binding interactions with the SARS-CoV-2 main protease (Mpro) and receptor-binding domain of the spike (S-RBD) protein, by using computational methods. Rutin, isoquercetin, and quercetin-3-O-glucuronide were shown to be the most potent inhibitors for Mpro and S-RBD with docking scores and Ki values ranging from -16.06 to -10.67 Kcal/mol and 0.005 to 30.01 nM, respectively. Evaluation of ADMET pharmacokinetic properties and the drug likeness in silico revealed that only 3,5-dicaffeoylquinic acid, 3–4–5-tricaffeoylquinic acid, isorhamnetin-3-O-glucoside, and rubescensin A could be more effective drugs against COVID-19. Molecular dynamics (MD) simulations (100 ns) and MM-GBSA calculations confirmed the stability of ligand-protein complexes via hydrogen bonding interactions with crucial residues. The analysis of structural parameters (RMSD, RMSF, H-bonds, Rg, and SASA) indicates that 3,4,5-tricaffeoylquinic acid and rubescensin A compounds have good stability and significant binding affinity with the Mpro and S-RBD protein. Taken together, our findings confirm that Artemisia campestris as a plausible source of anti-SARS-COV-2 phytochemicals and suggest that may play important role in this activity.