The part-nationalised lender said it is selling up to another 20% of the car and home insurer through a placing of shares with big institutions, as it takes advantage of buoyant stock market conditions.
RBS floated its insurance arm on the stock market as Direct Line Insurance Group last October, and its third deal to offload the insurer's shares could reduce its stake from 48.5% to 28.5% if all the shares are taken up.
Its announcement comes days after Chancellor George Osborne pulled the trigger on another major share sale, offloading 6% of Lloyds Banking Group for about £3.2 billion. Investors are also digesting Barclays' £5.8 billion rights issue.
RBS was forced to sell its insurance business as a condition of its £45 billion government bailout at the height of the financial crisis in 2008. Under European Union rules, it must sell the entire business by the end of next year.
Direct Line has brands including Green Flag and Privilege and insures almost one in five UK cars.
It recently emerged that around 2,000 jobs are under threat at the insurer, which is based in Bromley and employs 14,400 staff.
Shares in Direct Line closed at 218p, valuing the business at around £3.3 billion.
The 81% taxpayer-owned bank announced the sale after the market had closed and said it will not sell any more shares in the insurer for another 90 days after the placing completes.
RBS sold over a third of the insurer at the time of its flotation, with shares initially valued at 175p, and offloaded another 17% in March.