Kellock, who is now into his ninth season at the club, will continue to captain the side from the second-row.
The Warriors last outing was in the narrow defeat to Bath Rugby in the European Rugby Champions Cup in January.
Peter Murchie comes in at full-back, while DTH van der Merwe continues on the left wing and Lee Jones returns from injury on the opposite side.
Richie Vernon returns to the Warriors back-line after playing at Number 8 against Bath and he'll form a new centre partnership with Fraser Lyle, who will be making his Warriors debut, after joining the club in November.
After featuring for Scotland against France in the RBS 6 Nations last weekend, Peter Horne returns to the Warriors squad at fly-half and Niko Matawalu comes in at scrum-half.
In the front-row Alex Allan is at loose-head, Pat MacArthur continues at hooker and Mike Cusack is once again named at tight-head.
Tim Swinson returns from injury and starts in the second-row alongside Kellock.
James Eddie comes in at blind-side flanker, while Tyrone Holmes is back from injury at open-side and Leone Nakarawa moves to Number 8.
Rossouw de Klerk and Josh Strauss are also fit again and both are named on the bench, alongside Canadian international Connor Braid who re-joined the club on a short-term loan spell from London Scottish earlier this week.
Glasgow Warriors head coach Gregor Townsend said: "We're looking forward to returning to action after a three-week break, but we'll face a tough challenge over in Parma on Sunday afternoon.
"This is an opportunity for a number of players to show what they are capable of and I'm delighted for Fraser (Lyle), who will be making his debut for the club.
"Zebre have always given us a really tough game on their home patch and they've already beaten Edinburgh and Ulster and run Ospreys close at home this season.
"Sunday will be a special day for Al (Kellock) as he joins a special group of Warriors to make 150 appearances for the club and I'd like to congratulate him on reaching this milestone."
Glasgow Warriors team to play Zebre, GUINNESS PRO12, Stadio Sergio Lanfranchi, Sunday 15 February (kick-off 1pm UK time) - live on Sky Sports 1:
15. Peter Murchie
14. Lee Jones
13. Richie Vernon
12. Fraser Lyle
11. DTH van der Merwe
10. Peter Horne
9. Niko Matawalu
1. Alex Allan
2. Pat MacArthur
3. Mike Cusack
4. Tim Swinson
5. Al Kellock (Captain)
6. James Eddie
7. Tyrone Holmes
8. Leone Nakarawa
Replacements
16. Kevin Bryce
17. Jerry Yanuyanutawa
18. Rossouw de Klerk
19. Josh Strauss
20. Will Bordill
21. Ali Price
22. Connor Braid
23. Rory Hughes
Not available due to injury: Adam Ashe (neck), Chris Fusaro (ankle), Sean Maitland (shoulder), Henry Pyrgos (knee) and Duncan Weir (arm).
Guinness PRO12
Suite 208, Alexandra House,
The Sweepstakes
Ballsbridge, Dublin 4, Ireland