The event was organised by the All Under One Banner group, which describes its core aim as staging marches “at periodical intervals until Scotland is free”.
Police said around 2,000 marchers had joined the procession by 10.30am.
The march began at the Botanic Gardens in the city’s west end before making its way down Great Western Road. It arrived at George Square just before noon.
Marchers had to endure several torrential downpours as they made their way across the city.
Many pro-independence campaigners believe a second referendum is justified after the UK voted to leave the European Union last month - despite a majority of Scots backing continued membership.
Nicola Sturgeon said in a keynote speech last week that independence may offer the most “certainty and stability” for Scotland if the UK opts to quit the European Union, as expected.
The First Minister previously said a second referendum on whether Scotland should go it alone is “highly likely”.
But an opinion pull published on Thursday found almost a third of voters want to wait until the UK’s deal with the European Union (EU) is clear before deciding whether to hold another Scottish independence referendum.