The Justin Lin directed movie - taking over from JJ Abrams who was in a galaxy far far away at the time - takes $59 million on its opening weekend.
This year is the 50th anniversary of the TV series debut, but unfortunately this film has fallen short of its predecessors which both took in the $70 million or above region.
The new film has got far better reviews than Star Trek Into Darkness which could carry it onto a better gross in the long run.
The Secret Life of Pets falls to number 2 this week with a weekend gross of $29.3 million which brings the animated films total gross to $260 million.
Finding Dory is this week the highest total grossing movie and the longest running movie on the US top 10 with a $460 million total gross over 6 weeks.
Starring Seth Rogan and Zac Efron Bad Neighbours had no trouble de-throning the web slinger with an £8.5 million debut.
Spider-Man 2 falls into second place with £1.3 million bringing it's total gross to £22 million after 4 weeks.
Also new this week are:
Sabotage - Arnold Schwarzenegger's latest
La Cenerentola - the latest from the Met Opera
The Wind Rises
Before The Winter Chill
Last year saw the much anticipated Star Trek Into Darkness enter at the top knocking Iron Man 3 into second place.
Five years ago saw JJ Abrahams first Star Trek film enter the box office at the top knocking X-Men Origins: Wolverine into 3rd place with Coraline entering at 2.
Ten years ago had Van Helsing debuting at the top meaning Eternal Sunshine of The Spotless Mind fell to number 2.
Fifteen years ago had I Still Know What You Did Last Summer go to the top on it's first week leaving The Waterboy to have a single week at the top.
The Hangover Part III stayed at the top for a second weekend in a row this week with no competition from any new releases meaning the only movement in the top 5 was Star Trek into Darkness climbing 1 place and The Great Gatsby dropping a place.
Longest stay in the chart this week is The Croods which is now on an 11 week run and the highest grossing film is Iron Man 3 which has to date grossed £ 36,358,709 A year ago Ridley Scott brought his new Alien film to cinemas in the shape of Prometheus which debut at the top and was hence the highest new film knocking Men in Black 3 from the top.
Five years ago the first Sex and the City movie made it's debut at the top of the UK box office knocking the fourth instalment of the Indiana Jones franchise, The Kingdom of the Chrystal Skull from the top.
Ten years ago The Matrix Reloaded was still riding the wave of expectation at the top keeping Steve Martin at bay in the runner up spot in Bringing Down the House which debuted at 2.
Fifteen year ago meteor disaster movies were all the rage and Deep Impact was still at the top while horror film Wishmaster was the highest new film at 3.
Twenty years ago Indecent Proposal was proving to be the top grossing film of May.
Check out this weeks UK box office.
UK release date: 10th May 2013
Highest chart position: 1
Weeks on box office: 7
Total UK gross £25,543,789 and the 136th top grossing film in the UK
Total World gross $467,358,232 and the 180th top grossing film globally
UK BBFC Certificate: 12Genres: