The COVID-19 pandemic, caused by SARS-CoV-2, has led to catastrophic damage for global human health. The initial step of SARS-CoV-2 infection is the binding of the receptor-binding domain (RBD) in its spike protein to the ACE2 receptor in the host cell membrane. Constant evolution of SARS-CoV-2 generates new mutations across its genome including the coding region for the RBD in the spike protein. In addition to the well-known single mutation in the RBD, the recent new mutation strains with an RBD “double mutation” are causing new outbreaks globally, as represented by the delta strain containing RBD L452R/T478K. Although it is considered that the increased transmissibility of double-mutated strains could be attributed to the altered interaction between the RBD and ACE2 receptor, the molecular details remain to be elucidated. Using the methods of molecular dynamics simulation, superimposed structural comparison, free binding energy estimation, and antibody escaping, we investigated the relationship between the ACE2 receptor and the RBD double mutants of L452R/T478K (delta), L452R/E484Q (kappa), and E484K/N501Y (beta, gamma). The results demonstrated that each of the three RBD double mutants altered the RBD structure and enhanced the binding of the mutated RBD to ACE2 receptor. Together with the mutations in other parts of the virus genome, the double mutations increase the transmissibility of SARS-CoV-2 to host cells.