Directed by Lynne Ramsay, the film stars Tilda Swinton as the mother of a boy who carries out a high-school killing spree.
John Madden, chairman of the British Film Institute (BFI) jury, said: "We were simply bowled over by one film, a sublime, uncompromising tale of the torment that can stand in the place of love. We Need To Talk About Kevin is made with the kind of singular vision that links great directors across all the traditions of cinema."
The film's director described the award as "light at the end of the tunnel", adding: "It's been a few hard years. My dad passed away during this process... I wish he could be here tonight. We worked really hard on this one....It's a really major achievement for us, we have been wanting this for years."
Gillian Anderson, one of the judges for Best Film, said the film was a deserving winner but added: "There were a few that we did have to battle it out over the table."
Ralph Fiennes was also honoured, receiving the BFI Fellowship, alongside David Cronenberg.
The actor, who made his directing debut at the festival with Coriolanus, and the Canadian director, won the awards for their "outstanding contribution" to film over the years.
Candese Reid won best British newcomer for her portrayal of a young homeless woman in Junkhearts.
Pablo Giorgelli picked up the Sutherland award from Terry Gilliam for his directorial debut Las Acacias, while director Werner Herzog won best documentary for Into The Abyss.
The star-studded awards saw Michael Fassbender, Liam Neeson, Gillian Anderson and Sam Taylor-Wood walk down the red carpet at LSO St Luke's in central London.Suggest a correction