Norman Brinker, who served as an alternate for the U.S. show jumping team at the 1952 Helsinki Olympic Games and a prominent restaurateur, died June 9 from complications of pneumonia while on vacation in Colorado. He was 78.

Mr. Brinker was born into a life of horses in Denver, Colo. As a child, he worked in his family’s horse dealing business. He went on to serve in the Navy and graduated from San Diego State University (Calif.). In 1954, he competed in the World Modern Pentathlon Championships in Budapest, Hungary. In 1955, he married professional tennis player Maureen Connolly. After she died of cancer in 1969, he remarried three times.

Mr. Brinker, Dallas, Texas, made his living as an entrepreneur in the restaurant business. He retired in 2000 as chairman of Brinker International, a Dallas-based restaurant group comprising the chains Chili’s Grill & Bar, On The Border Mexican Grill & Cantina, Maggiano’s Little Italy and a minority stake in Romano’s Macaroni Grill.

Chief among Mr. Brinker’s new concepts for eateries was the salad bar, which he popularized at Steak & Ale starting in the late 1960s. Besides asking diners to get up from their tables to serve themselves from a salad buffet, the chain also stood out for its cheerful servers’ stock introduction, “Hi, my name is Dirk, and I’ll be your waiter tonight.”

A lifelong horseman, Mr. Brinker suffered 32 broken bones, was in a coma for three weeks and temporarily paralyzed after a polo accident in Florida in 1993. Doctors doubted he’d walk again, but Mr. Brinker was mobile and back at work within four months.

Mr. Brinker is survived by: daughters Cindy Brinker Simmons, Dallas, Texas; Brenda Brinker Bottum, San Francisco, Calif.; Christina Brinker Aschtgen, Seattle, Wash.; son Mark Brinker, Portland, Ore.; stepson Eric Brinker, Peoria, Ill.; fourth wife, Toni Brinker; and five grandchildren.