Method for the production of dextran comprising the following steps: prepare a culture medium containing the appropriated mixture and balance of ingredients, mainly after accurate selection of nature and concentration of carbon and nitrogen sources, with a specific initial pH, inoculate the culture medium with an appropriated quantity of bacteria strain (to standardize the production and avoid as much as possible the variability of the system) carry out the fermentation for a given time and at a given temperature precipitate the dextran to separate the product from the culture medium the bacteria strain is a strain of Weissella cibaria.