The resolution was passed 230-198 on Wednesday, largely along party lines. Four Democrats broke ranks to vote with all Republican lawmakers, Xinhua reported.
The resolution held Barr and Ross in contempt for refusing to provide documents to justify adding a citizenship question to the 2020 census when subpoenaed. The Trump administration had since dropped the effort to add the question into the census.
"The resolution that's before us today is about protecting our democracy. ... It is about protecting the integrity of this body," Congressman Elijah Cummings, chairman of the House Oversight and Reform Committee, said on the House floor.
This is the second time Barr was held in contempt of Congress. He was previously held in contempt for refusing to turn over the full and unredacted version of the Mueller report, which detailed findings of a two-year-long probe into collusion and obstruction of justice allegations against the Trump campaign and Trump administration.
Though House Speaker Nancy Pelosi warned of severe consequences for being held in contempt of Congress, Wednesday's vote was believed to be largely symbolic.
The vote came against the backdrop of an intense political fight between the White House and Democrats. U.S. President Donald Trump on Sunday fired a series of racially charged tweets at four Democratic lawmakers, and the Democrats responded by pushing through a resolution on Tuesday condemning Trump.
Earlier Wednesday an effort to impeach Trump in the House of Representatives was halted, despite winning the backing of nearly 100 lawmakers.
( With inputs from IANS )