COVID-19 has greatly affected public health and world economy. In this study, we analyzed 129 full-length genomes of SARS-CoV-2 viruses of a Canadian population during early phase of the pandemic. Phylogenetic analysis revealed three major paths of transmission of SARS-CoV-2 viruses into Canada. Twenty-one substitutions that have frequencies greater than 3% of viral population were identified. Analysis of these substitutions indicated that P1427I (ORF1b), Y1464C (ORF1b), and Q57H (ORF3a) might affect functions of the corresponding SARS-CoV-2 encoded proteins. Additionally, we found the evidence of positive selection on the ORF3a and codon 614 of Spike protein, suggesting the viral components responsible for host entry and activation of inflammation response were targeted by host immune responses. The study showed genomic variation and evolution of SARS-CoV-2 in a Canadian population. These information may help develop preventive strategies and be used for further study of SARS-CoV-2 pathogenesis and therapeutics development.