Film actor Peter Finch died yesterday in Los Angeles after apparently suffering a heart attack. The 60-year-old, four-time winner of the British Film Academy's award for best actor, and a strong contender for Oscar recognition this year for his performance in "Network," was stricken while sitting in the lobby of the Beverly Hills Hotel.

Paramedics from the Beverly Hills fire department were unable to revive Mr. Finch. He was taken to the Medical Center of the University of California at Los Angeles and placed in the intensive-care unit.

The report of his death several hours later came from the director of "Network," Sidney Lumet, whom Mr. Finch had been waiting to meet for breakfast, prior to a joint appearance on the television show, "Good Morning, America."

Mr. Finch had appeared on television Thursday night as a guest of Johnny Carson.

He gave one of the most impressive performances of his career in the role of Israeli Prime Minister Yitzhak Rabin in the television movie, "Raid on Entebbe," shown last Sunday night. There is a distinct, ironic possibility that Mr. Finch could win the best acting awards of both the motion picture and television academies within the next few months.

Mr. Finch was born in London in 1916, the son of the noted Australian physicist and mountaineer George Finch, a member of the Leigh-Mallory Everett expedition of 1922. Mr.Finch's parents were divorced in 1918, and he was reared by a grandmother in France and Madras, India.

Mr. Finch settled in Australia as a young man and worked at a variety of jobs while attempting to eke out a living during the depression. Eventually, he turned to acting in vaudeville, touring companies, radio and Australian movies, then virtually unknown outside that country.

According to film historian David Shipman, Mr. Finch's first important film role came opposite Cecil Kellaway in the 1938 Australian production, "Mr. Chedworth Steps Out."

Mr. Finch served with the Australian Army in the Middle East during World War II and later formed a stage troupe of Allied servicemen called "Finch's Follies."

Returning to Australia to resume his acting career, Mr. Finch became perhaps the best known radio actor in the country after founding a group named and patterned after Orson Welles' Mercury Theater Players.

When Laurence Olivier toured Australia in 1947, Mr. Finch met him and was urged to pursue an acting career in England. Upon his arrival thare a year later, Olivier arranged the audition that led to Mr. Finch's successful London theatrical debut opposite Edith Evans in "Daphne Laureole."

The first of Mr. Finch's movies to achieve international recognition was "The Overlanders," an action epic about frontier Australia directed by Harry Watt and released in 1948. Mr. Finch also had a featured role in that film's successor, "Eureka Stockade."

He made his English movie debut in 1949 in "Train of Events," and appeared subsequently in such pictures as "The Wooden Horse," "The Miniver Story and the Disney "Story of Robin Hood," in which he played the wicked Sheriff of Nottingham.

Mr. Finch won his first British Film Academy award in 1956 for "A Town Like Alice," an adaptation of a Nevil Shute novel. He repeated in 1960 for "The Trials of Oscar Wilde," in 1961 for "No Love for Johnnie," and in 1971 for "Sunday Bloody Sunday," a performance that also won him an Oscar nomination and brought best actor awards from the National Society of Film Critics and the New York Film Critics.

Mr. Finch made his American film debut in 1953 as Elizabeth Taylor's plantation-owning husband in "Elephant Walk," a box-office failure. He probably made his first significant impact on a large American movie public in 1954 when he played Rinaldi, the sternly attractive mission doctor who stirred Audrey Hepburn's Sister Luke in Fred Zinnemann's "The Nun's Story."

Mr. Finch recently moved to hollywood following several years of residence in Paris, Jamaica and Switzerland.

He is survived by his fourth wife, a former Jamaican beauty shop operator, Eletha Barret and their 9-year-old daughter, Diana and three grown children all residing in Europe, from earlier marriages.