We first conducted time-series analysis of mono- and dinucleotide composition for over 10,000 SARS-CoV-2 genomes, as well as over 1500 Zaire ebolavirus genomes, and found clear time-series changes in the compositions on a monthly basis, which should reflect viral adaptations for efficient growth in human cells. We next developed a sequence alignment free method that extensively searches for advantageous mutations and rank them in an increase level for their intrapopulation frequency. Time-series analysis of occurrences of oligonucleotides of diverse lengths for SARS-CoV-2 genomes revealed seven distinctive mutations that rapidly expanded their intrapopulation frequency and are thought to be candidates of advantageous mutations for the efficient growth in human cells. •Time-series change in mono- and dinucleotide compositions in SARS-CoV-2 genome•The time-series change found for SARS-CoV-2 differed from that of Zaire ebolavirus.•Sequence alignment-free method to search advantageous mutation in viral genomes•Seven mutations of SARS-CoV-2 rapidly expanding their population frequency•A method other than phylogenetic tree construction for viral evolutionary study