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.
Venezuela re-opens border with Colombia
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.
Venezuelans cross border
Growing discontent on the streets
Women push past border controls
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.
Venezuela has opened its border with Colombia for the second time this month to allow people to cross over to shop for basic foods and medicines.