Hopes are high that the vessel will be seaworthy within two years and allow those who built it to sail it.
"I work on it from 7:00 am to 3:00 pm, and more if we need it," says Slawomir Michalski, of his labour of love.
Sunny and mild spring weather now allows the work to go ahead full steam after a long, cold winter.
"It's like I'm building my own home," Michalski told AFP, of the 57-foot-long sailboat (17.8 metres).
Construction began a decade ago -- the brainchild of Father Boguslaw, a priest working at the Saint Lazarus shelter at the time and a former shipyard worker in the Baltic port city of Gdansk.
With technical knowledge and skills in shipbuilding, he was convinced that involving the homeless in the project would help win back their self-confidence, encourage teamwork and contribute towards their return to the workforce.
When the charismatic Father Boguslaw died in 2009, Michalski says that residents swore "on his grave" to complete the schooner, which will bear his name.
Shipbuilding is also in Michalski's blood.
Now aged 60, in the 1970s, he worked as a welder at the Lenin Shipyard in Gdansk just as the anti-communist Solidarity movement was taking shape, led by freedom icon Lech Walesa.
At the time, Walesa was just another electrician, but soon won the Nobel Peace Prize as the leader of Solidarity, the communist bloc's first and only free trade union that peacefully toppled the system in Poland, ushering in democracy in 1989.
Walesa became Poland's first freely elected post-World War II president a year later.
"I worked on the ship's hold, while Walesa was repairing the electric trolleys," Michalski recalls, of his shipyard days, as he welds metal parts of a door leading to the schooner's galley.
"We worked together, we were on strike together during the Solidarity era, and then I left everything behind and wound up in a homeless shelter," Michalski told AFP.
He has been living at the shelter in Warsaw's western Ursus district -- famous during the communist era for its tractor factory -- on and off since 2009, as he has battled with alcohol. But building the schooner has helped keep up his morale.
Run by the Roman Catholic order of the Camillian Fathers, the centre provides shelter for about 100 men over the age of 40, and squeezes more in on extra mattresses on the floor in winter.
"There were a lot of people wondering whether we weren't a little mad -- what a completely silly idea: homeless people are building a sailboat?" Michalski says, tapping his head.
"But they've seen the yacht grow from one year to the next, so people have changed how they think about it, and now they see it as a great idea," he added.
Polish shipbuilder Bogdan Malolepszy donated the blueprints for the two-masted BM-57 model schooner he designed himself, while other firms have furnished metal, cables, paint and other supplies.
Hopes are high that the vessel will be seaworthy within two years and allow those who built it to sail it, before then chartering it.
"Altogether with the bowsprit, the boat will be up to 63 feet long," said ship captain Waldemar Rzeznicki, checking the schooner's blueprints.
He devotedly oversees the work, day and night, on the grounds of the shelter.
"Just building it gives us strength, both to the homeless and us volunteers, because this work is happiness," Rzeznicki told AFP.
Michal Jedynak, another shelter resident, works on the staircase leading to the cabin, which will sleep 12 crew members.
But it has not been all smooth sailing.
"Michal is very strong, but an alcohol problem prevents him from working regularly," Rzeznicki notes.
The large, grey construction has progressed not only due to the hard work of the shelter's residents, but also thanks to private donors, including companies.
Inspired by the determination of the homeless shipbuilders, Tadeusz Wojtowicz, CEO of the Gdansk-based Sail Service company, says he is considering his firm sewing 170 square metres (203 square yards) of sails free of charge.
"If these people have the strength to carry out the project, we must admire them and support them.
"If they have the right motivation, people can achieve great things," Wojtowicz told AFP.
Finishing up his welding for the day, Michalski dreams of setting sail.
"If, in two years, I'm as well as I am now, if my health is the same, there'll be just one thing to do; we’ll have to hoist the sails and take off."