A 54-year-old Swedish schooner, which for the last five years has been a Caribbean cruise ship for the well-heeled, trimmed its massive reddish-brown sails and docked yesterday in its new home port of Alexandria.

The Lindo, with its towering oak masts and web of rope rigging, was recently donated by its New Jersey owners to a private, nonprofit foundation in Alexandria, ending the city's nearly decade-long search for a symbol of its maritime heritage.

Alexandria, like many cities along the Eastern Seaboard, has in recent years rediscovered the commercial and recreational potential of its waterfront. Currently, the city is involved in a multimillion dollar development project that has already brought a new art center, parking and office building to the Potomac River's edge of Old Town. By 1985, the project is expected to add major improvements to the city's rotting docks and construct a nearby plaza to include a market and restaurants.

"To a city like Alexandria, that began with a maritime tradition, a vessel like this keeps us in touch with out past," said Charlie Perry, a board member and a founder of the Alexandria Seaport Foundation. "This is something that should not be forgotten."

City officials had long explored ways of acquiring such a ship, said City Manager Douglas Harman. He said the city even considered a $1 million plan to build its own replica of the kind of 19th-century schooners that plied Alexandria's waters hauling import-export trade along the East Coast. But the plan was too costly and was abandoned.

But a year ago, shortly after a waterfront festival that featured a tall ship, some local businessmen formed the Alexandria Seaport Foundation, a tax-exempt, nonprofit organization to promote the public's interest in the city's seafaring past and began looking for a historic vessel for the city.

In December, the foundation learned that a deal to sell the Lindo to a private company in Norfolk collapsed. After months of talks with the foundation, the ship's owners, for whom the ship had become a financial burden, decided to donate the Lindo to the group.

Perry said he is hopeful that the $200,000 plus operating and maintenance cost of the Lindo will come from private and corporate donors.

Plans include charging the public a $2 fee to board the ship, now docked at the Torpedo Factory Pier at North Union and Cameron streets. U.S. Coast Guard regulations prohibit using the ship for excursions, according to a foundation spokesman.

City Council member Patricia Ticer said perhaps the city should consider ways it could directly support the ship.

"It's not that we have a lot of extra money hanging around, but the city could help financially," Ticer said.

That would be good news for Lindo's captain, G. Francis Birra, who said yesterday that he has a "moral commitment to see the boat in good hands."

Birra said he is hoping the Lindo's new owners will support the ship in next May's Trans-Atlantic Tall Ships Race, a six-week wind sprint from the south of France to Quebec. In 1976, the Lindo captured third place.

But none of that mattered to 12-year-old Antonio Moore who was perched on the dock's railing transfixed by the appearance of the Lindo. He dropped the rocks he was throwing at a turtle swimming among the waterfront's floating debris.

"I ain't never seen anything like that before," he said, momentarily forgetting about the turtle. "That's really something."