Last week 35,000 crossed over for the first time since the border was closed a year ago by President Nicolas Maduro to fight cross-border crime.
Officials said at least that many had entered Colombia on Saturday.
Many basic goods are in short supply in Venezuela because of a severe economic crisis in the country.
The border across a pedestrian bridge connecting Tachira in Venezuela and Cucuta in Colombia opened a day earlier than authorities from both countries had previously announced.
Officials said they wanted to avoid the build-up of too many people.
It was expected to stay open into Sunday.
Venezuela has suffered severe shortages for months as a result of the falling price of oil which is the country’s prime source of income.
Many supermarket have empty shelves and Venezuelans spend days in queues to buy basic goods.
Government critics also blame President Maduro for severe mismanagement of the economy.
Mr Maduro for his part has blamed the country’s business community for the shortages.
He ordered the border to be closed in August 2015 after former Colombian paramilitaries attacked a Venezuelan military patrol and wounded three soldiers.