Greenlaw was born in Connecticut, the daughter of Jim and Martha Greenlaw. Her father was an information systems manager for Bath Iron Works. She was raised in Topsham, Maine, and her family spent their summers in Isle au Haut, a village of 70 people off the coast of Maine. Greenlaw attended Colby College, where she majored in both English and government. During the summer after her freshman year she became a cook and deckhand on the fishing boat Walter Leeman. She continued working on the boat during free time and vacations, and after her graduation in 1983. The owner of the boat, Alden Leeman, installed Greenlaw as a swordfish captain in 1986, when he bought a second boat.

Greenlaw wrote in The Hungry Ocean: "Being a woman hasn't been a big deal. I never anticipated problems stemming from being female, and never encountered any. I have been surprised, even embarrassed, by the number of people who are genuinely amazed that a woman might be capable of running a fishing boat."

Greenlaw was the captain of the Hannah Boden, which was the sister ship of the Andrea Gail, which foundered in the Atlantic in the 1991 Perfect Storm. Greenlaw's efforts to warn the Andrea Gail about the impending storm were portrayed in Sebastian Junger's 1997 book The Perfect Storm and in the movie version, in which she was played by Mary Elizabeth Mastrantonio.

Junger called Greenlaw not just the only female swordfishing captain, but "one of the best captains, period, on the entire East Coast."

In 1997, Greenlaw settled in Isle au Haut, and bought a lobster boat, the 35-foot Mattie Belle.

Greenlaw's first book, The Hungry Ocean, described a one-month swordfishing voyage, entailing, "among other things, treacherous weather, uncooperative fish, wildly entertaining shipmates, and the exhausting, mind-bending pressure of ten consecutive 21-hour days."

Kirkus Reviews called All Fishermen Are Liars "a crackling collection of fishing yarns." The New York Times review of the book said that Greenlaw "is a terrific spinner of sea stories" but that the book was hampered by her being "awkward and uncomfortable describing her emotions."

Time magazine called her Recipes From a Very Small Island, co-authored with her mother, a "must-have cookbook."

On May 28, 2009, Greenlaw was convicted of illegally entering and illegally fishing in Canadian waters by the Newfoundland Provincial Court. The Crown asked for a fine of CAD$53,000, while the Defence recommended a fine of half that amount. She was fined $38,000 after the judge found she did not use "due diligence". According to Greenlaw, "It's a lot of money to be writing a check ... but beyond the money, I've been convicted of two offences." She had expected to be acquitted.

Greenlaw has also recently published two novels of detective fiction, Slipknot and Fisherman's Bend, featuring her fictional detective Jane Bunker.

Greenlaw is the winner of the U.S. Maritime Literature Award in 2003 and the New England Book Award for nonfiction in 2004.