"As far as we have heard from our sources, NLD candidates won in all 44 seats. I think the Election Commission will come up with official announcements soon," NLD campaign manager Nyan Win told Reuters.
It also reported that the victory claim was displayed in a large digital board outside the headquarters of NLD in Myanmar.
Thousands of pro-democratic supporters gathered at the NLD party headquarters, waving red flags and shouting slogans, "We Won! We Won!".
Meanwhile, amidst NLD's clean swept, the United States and European Union had hinted they could lift some sanctions - imposed over the past two decades in response to human rights abuses - if the election was free and fair.
After the Sunday election, the 66-year-old Nobel Peace Prize laureate issued a statement asking supporters to respect other parties.
"It is natural that the NLD members and their supporters are joyous at this point. However, it is necessary to avoid manners and actions that will make the other parties and members upset. It is very important that NLD members take special care that the success of the people is a dignified one," said Suu Kyi.
10 Points About 2012 By-Election:
Military took power in a 1962 coup
The military government called a widely criticized general election in 1990. NLD won the election but the result was nullified.
Almost after 15 years of house arrest, Suu Kyi was freed from house arrest in Nov. 1, 2010
March 30, 2011 President Thein Sein, a general in the former junta assumed office.
The president made dramatic reformation. He freed hundreds of political leaders including Suu Kyi in a year.
U.S secretary of state Hillary Clinton made the first visit to the country by a U.S. secretary of state since 1955.
18 January 2012, Suu Kyi formally registered to contest a Pyithu Hluttaw(lower house) seat in the Kawhmu Township
During a mass election campaign in Mandalay, Suu Kyi unexpectedly left after 15 minutes, because of exhaustion and airsickness on March 3, 2012.
On 14 March 2012, Suu Kyi publicly campaigned for reform of the 2008 Constitution
NLD announced it had won 44 seats out the 45 vacant parliament seats in 2012 elections on April 1, 2012