With only two games of the regular Magners League season remaining - Sunday's match, then an away fixture against leaders Leinster the second weekend in May - it's imperative that Edinburgh post victories if they are to propel themselves from their current fifth place into the top four and a guaranteed play-off place.
Grant is among four changes, one positional, from the team that started last weekend's dismal away defeat against Newport Gwent Dragons.
The other alterations see international centre Nick De Luca return from injury to start at outside centre; Greig Laidlaw starting at scrum-half with Mike Blair reverting to the bench (the position from which he exerted considerable influence in Edinburgh's league win at Ravenhill last September); and Ben Cairns moving from centre to full-back in place of Jim Thompson who is on the bench.
Edinburgh's head coach Rob Moffat said: "Roddy has been one of our most consistent players this season. He sets high standards for himself and I believe he will demand that of others.
"As a coach you are always looking for leaders, people who are willing to accept responsibility, and Roddy has those characteristics in droves."
Grant, who has skippered the Scotland 7s side on the IRB circuit and represented Scotland A, said today: "I'm proud to have been asked to lead the team but Sunday is about the entire Edinburgh squad setting out our stall and putting in a performance that means we can still strive for that play-off place.
"We've faced Ulster on three occasions this season so far, as they were in our pool in the Heineken Cup, and they've all been close-fought matches, with a real Titanic battle for possession up front and I believe it will be along similar lines this weekend."
Edinburgh are without two players who played at Rodney Parade last Sunday. Flanker Ross Rennie (hamstring) and winger Simon Webster (Achilles) join long-term casualties Simon Cross and Andrew Easson (both knee), Chris Paterson (kidney), Craig Hamilton (head knock) and Ross Samson (arm) on the not considered due to injury list.
Edinburgh Rugby Club v Ulster at Murrayfield in the Magners League on Sunday 25 April, kick-off 4.05pm
15 Ben Cairns
14 Tim Visser
13 Nick De Luca
12 John Houston
11 Mark Robertson
10 Phil Godman
9 Greig Laidlaw
1 Allan Jacobsen
2 Ross Ford
3 Geoff Cross
4 Scott MacLeod
5 Jim Hamilton
6 Alan MacDonald
8 Dave Callam
7 Roddy Grant captain
Substitutes: 16 Andrew Kelly, 17 Kyle Traynor, 18 Fraser McKenzie, 19 Scott Newlands, 20 Mike Blair, 21 Andrew Turnbull, 22 Jim Thompson
Tickets are available by calling 0131 346 5180 or online at www.edinburghrugby.org.
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