The London-listed trust, which has a market capitalisation of 1.1 billion pounds ($1.4 billion), said on Wednesday the move followed disappointing returns due to "a number of stock-specific issues". It said it has appointed Majedie Asset Management as its new manager, with James de Uphaugh as the portfolio manager.
Holdings in Eddie Stobart, Amigo and Burford Capital had been particularly poor performers, the trust's chairman Glen Suarez told Reuters.
Barnett, head of UK equities at Invesco, worked with veteran fund manager Neil Woodford at Invesco before Woodford left to set up his own now-closed firm, and has come under pressure this year.
Adrian Lowcock, head of personal investing at investment platform Willis Owen, said the trust had "finally run out of patience with Barnett’s contrarian style".
The trust posted a 3.1% fall in net asset value in the six months to Sept. 30. Its shares were unchanged at 603 pence at 1030 GMT, compared with a 0.7% fall in the FTSE 250 index. In the year to date, shares in the trust are up 1.2%, lagging an 18% gain in the FTSE 250.
Invesco said in a statement that it was "disappointed", but had no plans to change the way it invested.
"We remain of the conviction that our investment strategy is sound," it said. "We believe there will be a revision of current market consensus and that we are on the cusp of this potential being realised."
The replacement of Invesco as manager comes a day before a British election expected to result in a majority for the ruling Conservatives, a prospect which has boosted the pound.
"We are not changing the focus on UK equities - to the extent there is a bounce in the UK, this portfolio has the same opportunities to profit from it," Suarez said.
Invesco last month appointed long-serving Invesco fund manager Martin Walker to act as co-head of UK equities alongside Barnett. The move followed a year of heavy outflows from funds managed by Barnett as well as by the broader group.
Barnett's UK Strategic Income, High Income and Income funds saw combined outflows of just over 2 billion pounds in the 12 months to Sept. 30, data from industry tracker Morningstar showed.
By Carolyn Cohn and Simon Jessop