Baugh was born in Gainesville, Florida. As a child she won the National PeeWee Golf Championship five times, her first coming at age three. Her parents divorced when she was 11 years old, and she moved with her mother from their Florida home to Long Beach, California. Her father Hale Baugh, a lawyer, was a very good amateur golfer, who introduced his children to golf at early ages. Her older brother Beau Baugh played professionally for a time. She graduated from high school at the age of 16 with excellent grades. She studied at Long Beach City College and California State University, Long Beach. Lacking the money to pay green fees, she and friends would sneak onto golf courses to play. At age 14 she won her first of two straight Los Angeles Women's City Golf Championships.

In 1971, at age 16, at the Atlanta Country Club in Atlanta, Georgia, she defeated Beth Barry in the 36-hole final match to win the U.S. Women's Amateur, becoming the youngest champion in the event's 76-year history to that stage. Her physical appearance brought her considerable publicity, and for 1971 she was chosen as a Los Angeles Times "Woman of the Year". In 1972 she won Golf Digest's "Most Beautiful Golfer." She made a television commercial for UltraBrite toothpaste that won a Clio Award. Baugh was a member of the U.S. teams that won the 1972 Curtis Cup and the 1972 Espirito Santo Trophy.

She had been offered a full academic scholarship to Stanford University, but declined this opportunity, as Stanford did not have a women's golf team at that point. She then turned professional in late 1972, and played several pro events in Japan, where her appearance attracted immense interest and publicity. She had not yet turned 18 at this stage, so was ineligible to join the LPGA Tour, but was eligible to play in Japan. She earned her LPGA Tour card on her first attempt in 1973, and the very next week placed second in her Tour debut. She earned 1973 Rookie of the Year honors.

Despite her successful start and prodigious talent, alcoholism and emotional problems would take over her life, and she would never win an LPGA tournament. Her drinking caused spontaneous bleeding that could have ended her life, had she not sought treatment that included time at the Betty Ford Clinic in 1996. She described her battle with alcohol in a 1999 book titled "Out of the Rough."

During her professional golf career from 1973 through 2001, Baugh earned 71 top-10 finishes, including ten runner-ups. She earned significant prize money, and supplemented this with even greater earnings from endorsements and golf outings, after signing with the International Management Group upon turning professional. She became a member of the Women's Senior Golf Tour, and has also worked as a television announcer for The Golf Channel. She operates "Laura Baugh Golf Workshops for Women Only".[1]

Baugh has been married four times, twice to Bobby Cole, the father of her seven children.