Iran was among countries which was hard hit at the early stage of the coronavirus disease 2019 (COVID-19) pandemic and dealt with the second wave of the pandemic in May and June 2020; however, there are a very limited number of complete genome sequences of acute respiratory syndrome coronavirus 2 (SARS-CoV-2) from Iran. In this study, complete genome sequences of the virus in the samples obtained from three patients in Alborz province in May and June 2020 were generated and analyzed using bioinformatic methods. The sequenced genomes were positioned in a cluster with B.4 lineage along with the sequences from other countries namely, Turkey, United Arab Emirates and China. There were seven single nucleotide variations (SNVs) in common in all samples and only one of the sequenced genomes showed the D614G amino acid substitution. Three SNVs, 1397 G>A, 28688 T>C, 29742 G>T, which had already been reported in February, were found with high frequency in all the sequenced genomes in this study, implying that viral diversity reflected in the early stages of viral transmission in Iran were established in the second wave. Considering the importance of molecular epidemiology in response to ongoing pandemic, there is an urgent need for more complete genome sequencing and comprehensive analyses to gain insight into the transmission, adaptation and evolution of the virus in Iran.