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.