The days out on the Torbay Express will take place on 10 dates through July, August and September 2006.
The train is made up of 1950s-style carriages and will be hauled by Great Western locomotive King Edward I.
The trip will get under way at Bristol Temple Meads and visit Weston-super-Mare, Taunton, Exeter St Davids, Paignton and Kingswear.
It will then travel on to Kingswear on the Paignton and Dartmouth Railway.
The director of Part-Time Rail, which is organising the trip, said it was a good chance to see some of a great engineer's work up-close.
"There is the additional bonus that in this bi-centenary commemorative year since railway architect Isambard Kingdom Brunel's birth, the trip offers an opportunity experience a steam trip over some of his handiwork."
The King Edward 1 will run on the following dates:
- Sundays 16, 23 & 30 July
- Every Sunday in August
- Saturdays 29 July & August 12
- Sunday September 3
- Trains depart Temple Meads at 0920, Weston 0945, Taunton 1105, Exeter 1200, Paignton 12.45, Kingswear 1320.
- On the way back: Kingswear 1710, Paington 1755, Exeter 1850, Taunton 2025, Weston 2110, Bristol TM 2140.