Newly-promoted City will take on Leeds at home in the Championship looking to win their first competitive game of the season.
Steve Cotterill’s side lost 2-0 to Sheffield Wednesday away from home on the opening weekend of the season, before going down 3-1 at Luton Town in the first round of the League Cup.
Then on Saturday, Brentford eased past City 4-2 at the Ashton Gate Stadium.
West Yorkshire outfit Leeds have also started the season disappointingly and have yet to win a competitive match.
The Whites played out a 1-1 draw with Burnley at Elland Road in their first Championship game of the season, before losing the League Cup first-round tie to Doncaster Rovers away from home.
Then on Sunday afternoon, Leeds played out a goalless draw with Reading away from home at the Madjeski Stadium.
Holloway believes that City will edge past Leeds at home and has predicted a 1-0 win for the Robins.
“It’s been a tough start for Bristol City,” the 52-year-old wrote on Skysports.com. “They were 2-1 up before they had a man sent off against Brentford.
“City were brilliant at home last year and I think it’s only a matter of time before they get it going. I think they’ll nick this one and they’ll finish higher than people think.”