Severe acute respiratory syndrome coronavirus 2 (SARS‐CoV‐2) is continuously evolving. Although several vaccines were approved, this pandemic is still a major threat to public life. Till date, no established therapies are available against SARS‐CoV‐2. Peptide inhibitors hold great promise for this viral pathogen due to their efficacy, safety, and specificity. In this study, seventeen antiviral peptides which were known to inhibit SARS‐CoV‐1 are collected and computationally screened against heptad repeat 1 (HR1) of the SARS‐CoV‐2 spike protein (S2). Out of 17 peptides, Fp13 and Fp14 showed better binding affinity toward HR1 compared to a control peptide EK1 (a modified pan‐coronavirus fusion inhibitor) in molecular docking. To explore the time‐dependent interactions of the fusion peptide with HR1, molecular dynamics simulation was performed incorporating lipid membrane. During 100 ns MD simulation, structural and energy parameters of Fp13‐HR1 and Fp14‐HR1 complexes demonstrated lower fluctuations compared to the control EK1‐HR1 complex. Furthermore, principal component analysis and free energy landscape study revealed that these two peptides (Fp13 and Fp14) strongly bind to the HR1 with higher affinity than that of control EK1. Tyr917, Asn919, Gln926, lys933, and Gln949 residues in HR1 protein were found to be crucial residues for peptide interaction. Notably, Fp13, Fp14 showed reasonably better binding free energy and hydrogen bond contribution than that of EK1. Taken together, Fp13 and Fp14 peptides may be highly specific for HR1 which can potentially prevent the formation of the fusion core and could be further developed as therapeutics for treatment or prophylaxis of SARS‐CoV‐2 infection. SARS CoV‐2 uses spike protein for binding with host cell membrane to entry. Spike protein consists of two domains such as S1 and S2. When S1 domain binds with host cell receptor ACE2, it is cleaved by host cell protease enzyme TMPRSS2. After cleavage of S1, S2 is inserted to the host cell membrane surface. Mainly HR1 and HR2 protein of S2 of SARS CoV‐2 spike protein are responsible for fusion process. After the insertion of S2 on host cell membrane, HR1 and HR2 are attached together, forming a fusion core to bring virus and cell membrane in close proximity to mediate fusion process. The outcome of this computational study displays that the attachment of peptide with HR1 protein can be good strategy to inhibit the formation of fusion core which may lead disruption of fusion process of SARS CoV‐2.