Yorkshire begin their Royal London 50-over campaign tomorrow against Gloucestershire at Scarborough (10.30 start).
The club will be looking to improve on their T20 showing, when they failed to reach the knockout stages, and Gillespie is adamant they can do just that.
“We’re determined to perform well in the tournament,” he said. “We feel we can have an impact.
“We’re really excited about it, really looking forward to it.
“We’re going to give it a really good go.”
Yorkshire gave it a good go last summer, when they finished top of their group with six victories from eight games.
But they fell at the first knockout hurdle when they lost to Durham at Headingley in the quarter-finals.
This year’s competition, which sees Yorkshire play four games in the next five days as they also travel to Derby on Monday, The Oval on Wednesday and Worcester on Thursday, could benefit from a surge of interest in 50-over cricket.
The recent World Cup in Australia and New Zealand revitalised the format, and Gillespie hopes fans will come out in force.
“I hope there’s a big knock-on effect,” he said.
“I hope we get as many people coming to watch the games as possible – not just at our county, but at all counties.
“The way that World Cup was played, the cricket that was played, was full of positivity.
“Conditions are very different in the UK in terms of the pitches and the weather, and it will be interesting to see what sort of pitches are prepared by counties, especially with squares getting a bit tired towards the back end of the summer, but I think 50-over cricket is a fantastic format.”
With the group stage condensed into a short time period, Gillespie plans to rotate his squad.
Yorkshire play seven games in the next 11 days overall, before their final group game on August 18.
“The schedule will be a challenge,” said Gillespie.
“It would be unrealistic to expect everyone to play in each and every game.
“It’s going to be a massive test for the players.
“We will manage the workloads as best we can.”
Key to Yorkshire’s chances could be Glenn Maxwell, the Australian batsman who shone during the World Cup.
Maxwell has struggled at times this summer in T20, but his one-day credentials are not in doubt.
“We’ve got Maxi until he links up with Australia in late August,” said Gillespie.
“He’ll be in with a chance of playing in the next Championship game, too, with Jonny Bairstow away with England.”
Yorkshire (from): Ballance, Bresnan, Brooks, Carver, Fisher, Gale (captain), Gibson, Hodd, Leaning, Lees, Maxwell, Patterson, Plunkett, Pyrah, Rhodes.