The evolution rate and genetic changes that occur during chronic infection with Helicobacter pylori have been analysed, but little is known about the genomic changes during the initial, acute bacterial infection phase. Here we analyse the rate and pattern of genome evolution in H. pylori from the genomes of two input strains isolated from human volunteers with asymptomatic infection, and the genomes of two output strains collected 20 and 44 days after re-infection. Similarly, we analyse genome evolution in bacteria from the genome sequences of input and output strains sequentially taken after experimental infection of a rhesus macaque. The estimated mutation rate reveals a mutation burst during the acute infection phase that is over 10 times faster than the mutation rate during chronic infection, and orders of magnitude faster than mutation rates in any other bacteria. The elevated frequency of mutations in outer membrane protein genes suggests that the mutation burst facilitates rapid host adaptation of the bacteria.