OBJECTIVE: To analyze the evolution and variation of SARS-CoV-2 during the epidemic starting at the end of 2019. METHODS: We downloaded the full-length genome sequence of SARS-CoV-2 from the databases of GISAID and NCBI. Using the software for bioinformatics including MEGA-X, BEAST, and TempEst, we constructed the genomic evolution tree, inferred the time evolution signal of the virus, calculated the tMRCA time of the virus and analyzed the selection pressure of the virus during evolution. RESULTS: The phylogenetic tree showed that SARS-CoV-2 belonged to the Sarbecovirus subgenus of beta Coronavirus genus together with bat coronavirus BetaCoV/bat/Yunnan/RaTG13/2013, bat-SL-CoVZC45, bat-SL-CoVZXC21 and SARS-CoV. The genomic sequences of SARS-CoV-2 isolated from the ongoing epidemic showed a weak time evolution signal with an average tMRCA time of 73 days (95% CI: 38.9-119.3 days). No positive time evolution signal was found between SARS-CoV-2 and BetaCoV/bat/Yunnan/RaTG13/2013, but the former virus had a strong positive temporal evolution relationship with bat-SL-CoVZC45 and SARS-CoV. The major cause for mutations of SARS-CoV-2 was the pressure of purification selection during the epidemic. CONCLUSIONS: SARS-CoV-2 may have emerged as early as November, 2019, originating most likely from bat-associated coronavirus. This finding may provide evidence for tracing the sources and evolution of the virus.