The transactions will be carried out between July 28 and August 26 either through order matching or put through.
Their value will be around VND287 billion (US$12.27 million).
The SSB share price has dropped by nearly 11 percent so far this year.
A SeaBank media representative told VnExpress that the four are senior executives who have a long-term commitment toward the company and would continue to own shares.
The bank is set to issue 59.4 million shares at the end of this quarter as part of its employee stock ownership plan.
Earlier this month another deputy director, Nguyen Thi Nga, bought 2.8 million shares to increase her stake to over 3.4 percent.
Around the same time her daughter Le Thu Thuy was replaced by Faussier Loic Michel Marc as the bank’s CEO.
But Thuy remains deputy chairwoman.