In December 2019, the novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) emerged in the province of Wuhan, China. Since then, it has spread worldwide with new mutations being reported. We performed genomic analysis to identify the changes in genetic diversity of SARS-CoV-2 between December 2019 and November 2020, and through molecular surveillance, we monitored the mutations that could be involved in viral fitness. We analyzed 2,213 complete genomes from 6 geographical regions worldwide, which were downloaded from GenBank and GISAID databases. Although SARS-CoV-2 presented low genetic diversity, there has been an increase over time, with the presence of several hotspot mutations throughout its genome. We identified 7 frequent mutations that resulted in non-synonymous substitutions (dN). Two of them, C14408T>P323L and A23403G>D614G, located in the nsp12 and Spike protein, respectively, emerged early in the pandemic and showed a considerable increase in frequency over time. Two other mutations, A1163T>I120F in nsp2 and G22992A>S477N in the Spike protein emerged recently and have spread in Oceania and Europe. Continuous molecular surveillance of SARS-CoV-2 will be necessary to detect and describe the transmission dynamics of new variants of the virus with clinical relevance. This information is important to improve programs to control the virus.