The hosts needed four wickets and Gloucestershire 64 runs to win an absorbing Division Two game but the final day's play was abandoned at 1.45pm.
Rain had fallen steadily since early morning and with no prospect of an improvement in time to get the ground fit, umpires Russell Warren and Martin Saggers made their inevitable decision. Both sides take eight points each.
Sussex, still searching for their first Championship win of the season, take on Middlesex at Hove on Friday.
Sussex coach Jason Gillespie said: "I thought we fought pretty hard in what were challenging conditions for both teams. I was pleased with a lot of what we did, especially the intent we showed when we batted in the second innings. We committed to our plans, were aggressive and positive and although plans don't always come off I was pleased we stuck to them because it will hold us in good stead going forward.
"We bowled well in their second innings and it was disappointing we've had no play and I'm sure Gloucestershire will also feel they were well in the hunt to win. We fancied our chances, although we weren't taking anything for granted. Overall we're doing pretty well. We've had three draws but in each of them we've had the opportunity to win so the signs are good."