The invention relates to a method for the production of a carboxylic acid from a primary alcohol, said method comprising: a first step of growing a strain of bacterium of the genus Acetobacter capable of selectively oxidizing said alcohol into said carboxylic acid, in an appropriate growth medium comprising glycerol as carbon source, until said bacterium reaches a late exponential growth phase; then a selective oxidation step comprising aerobically culturing said bacterium in a bioconversion reactor containing an appropriate liquid bioconversion medium containing said alcohol and glycerol, for a sufficient time to oxidize said alcohol into said carboxylic acid.