The House vote paves the way for the veto amendment to go on the ballot in the November general elections.
The measure was approved in the last legislature by both chambers and this is the second round of approval as required for any constitutional amendment.
At present the veto override power rests with the Secretary of the Interior.
If the governor vetoes a bill, he sends it back to the Fono.
If it is re-passed by each chamber, then the governor has the option of approving it or sending it to the Secretary of the Interior for a final decision.
The Secretary can either overrule or uphold the veto.
Under the amendment, a bill vetoed by the governor can become law if it is re-passed by the Senate and House by a two thirds majority in each chamber.
The veto override measure was last on the ballot was in the 2014 general elections.