The 19-year-old also won five silver medals at the event.
Her two male teammates, Tran Duy Khoi and Huynh Man Dat , each brought home three gold medals.
Another girl in the team, Nguyen Diep Phuong Tram pocketed two gold medals.
The Asian Age Swimming Championships took place in Bangkok from October 1-4 with three age brackets: Group A featured swimmers aged 18 and over, Group B included those aged 15 to 17 and Group C for swimmers aged 14 and below.
Each age bracket competed in 44 events (22 event for boys and 22 for girls).
After the championship, Vien will fly to the Republic of Korea to compete in the World Military Games from October 7-10.