'The Shape of Water' and 'Get Out' also are among the winners; the awards will be handed out Jan. 13 at the group's annual dinner.
Call Me by Your Name has been chosen as best picture by the Los Angeles Film Critics Association. The group met Sunday to vote on their picks for the year's best.
Call Me by Your Name won a total of three awards, including best director for Luca Guadagnino — a tie with Guillermo del Toro for The Shape of Water — and best actor for Timothée Chalamet.
The Shape of Water also won three awards, including best actress for Sally Hawkins and best cinematography for Dan Laustsen.
Among other winners, The Florida Project's Willem Dafoe and Lady Bird's Laurie Metcalf were named best supporting actor and actress, respectively. Jordan Peele won best screenplay honors for Get Out.
As previously announced, LAFCA chose Max von Sydow as the recipient of this year’s Career Achievement Award.
The awards will be handed out at the group's annual dinner, set for Saturday, Jan. 13, at the InterContinental Hotel in Century City.
A list of winners follows.
Picture: Call Me by Your Name
Runner-up: The Florida Project
Actress: Sally Hawkins, The Shape of Water
Runner-up: Frances McDormand, Three Billboards Outside Ebbing, Missouri
Actor: Timothée Chalamet, Call Me by Your Name
Runner-up: James Franco, The Disaster Artist
Supporting actress: Laurie Metcalf, Lady Bird
Runner-up: Mary J. Blige, Mudbound
Supporting actor: Willem Dafoe, The Florida Project
Runner-up: Sam Rockwell, Three Billboards Outside Ebbing, Missouri
Foreign-language film: BPM (Beats Per Minute) and Loveless (tie)
Runner-up: Martin McDonagh, Three Billboards Outside Ebbing, Missouri
Editing: Lee Smith, Dunkirk
Runner-up: Tatiana S. Riegel, I, Tonya
Production design: Dennis Gassner, Blade Runner 2049
Runner-up: Paul D. Austerberry, The Shape of Water
Cinematography: Dan Laustsen, The Shape of Water
Runner-up: Roger Deakins, Blade Runner 2049
Douglas Edwards Independent/Experimental Film/Video Prize: Lee Anne Schmitt's Purge This Land
Career Achievement Award: Max von Sydow
New Generation: Greta Gerwig