It sold the shares, equivalent to a 49% stake, through an auction at VND10,500 ($0.43) for a total of VND139 billion.
SHG currently trades at around VND3,100 on the market.
The shares were bought by an organization and individual each.
Song Hong has been making losses for the last four years and not organized an annual general meeting for two years.
Trading in its shares is therefore restricted to Fridays.
Song Hong specializes in constructing buildings, transport infrastructure and industrial parks.
It participated in the construction of the Noi Bai International Airport in Hanoi, a sports complex in Da Nang City and a paper factory in the northern province of Phu Tho.
It sold nearly seven million shares to the public in 2009. It was doing well between 2008 and 2010, with revenue reaching a peak of VND3.9 trillion in 2010.
But its performance has been declining since. Last year, it reported revenues of VND38 billion and losses of VND178 billion.