The hosts, who entered the tournament as favourites and top of the world rankings, will move to the brink of the semi-finals with victory against Sri Lanka on Friday, reports BBC.
"We know we have been great - not just good, but great - for four years," Moeen told BBC Sport.
"We want a trophy to top it all off. We'll give everything for it."
England's transformation from being dumped out of the 2015 World Cup in the first round has been built on the power of their batting line-up.
That was evident in Tuesday's win over Afghanistan at Old Trafford, where captain Eoin Morgan hit 17 sixes as part of a team total of 25 - both records for one-day internationals.
"Once we get going, it's almost unstoppable and that's the great thing about the team," added Worcestershire's Moeen.
"The likes of Morgan, Jos Buttler and Jason Roy - we have so many players, almost everybody in the top eight can do it."
Moeen returned to the side for the defeat of Afghanistan having been left out of the victories over Bangladesh and West Indies.
He struck an unbeaten 31 from nine balls and is in line to play his 100th ODI at Headingley.
"When I look back, I think back of the fun that I've had," said the 32-year-old. "All of a sudden, 100 games have come almost in the blink of an eye. It's been an amazing journey and hopefully we can finish it off with the World Cup."
Moeen's time out of the side coincided with the birth of his second child, a daughter named Haadiya.
"It's obviously amazing, great to have an addition to the family," he said. "She is sleeping, but I've not seen her a for a few days. My wife is doing all the hard work.
"It has added an extra bit of happiness in my life with everything that is going on. It is an amazing miracle and you realise how important family is to you.
"You know how hard it can be for the mother and you have to be there to be supportive. You put cricket and the World Cup to the back seat as much as you can."
A win on Friday would be England's fifth from six World Cup games and would put them on 10 points, possibly enough for a place in the semis.
From Leeds, they move on to play Australia, India and New Zealand; the other members of the top four and the teams likely to make up the semi-finals.
Sri Lanka have won only one of their first five games, but have four points because two of their matches have been abandoned.