With the progression of the global SARS-CoV-2 pandemic, the new variants have become more infectious and continue spreading at a higher rate than pre-existing ones. Thus, we conducted a study to explore the epidemiology of emerging variants of SARS-CoV-2 that circulated in Bangladesh from December 2020 to September 2021, representing the 2nd and 3rd waves. We collected new cases and deaths per million daily data with the reproduction rate. We retrieved 928 SARS-CoV-2 sequences from GISAID and performed phylogenetic tree construction and mutation analysis. Case counts were lower initially at the end of 2020, during January–February and April–May 2021, whereas the death toll reached the highest value of 1.587 per million on the first week of August and then started to decline. All the variants (α, β, δ, η) were prevalent in the capital city, Dhaka, with dispersion to large cities, such as Sylhet and Chattogram. The B.1.1.25 lineage was prevalent during December 2020, but the B.1.617.2/δ variant was later followed by the B.1.351/β variant. The phylogeny revealed that the various strains found in Bangladesh could be from numerous countries. The intra-cluster and inter-cluster communication began in Bangladesh soon after the virus arrived. The prominent amino acid substitution was D614G from December 2020 to July 2021 (93.5 to 100%). From February–April, one of the VOC’s important mutations, N501Y substitution, was also estimated at 51.8%, 76.1%, and 65.1% for the α, β and γ variants, respectively. The γ variant’s unique mutation K417T was detected only at 1.8% in February. Another frequent mutation was P681R, a salient feature of the δ variant, detected in June (88.2%) and July (100%). Furthermore, only one γ variant was detected during the entire second and third wave, whereas no η variant was observed in this period. This rapid growth in the number of variants identified across Bangladesh shows virus adaptation and a lack of strict quarantine, prompting periodic genomic surveillance to foresee the spread of new variants, if any, and to take preventive measures as soon as possible.