It is the first time the charity Marie Curie Cancer Care has run such a campaign in the Lothians, with a target of 150,000 in a year.
The organisation's nursing project helped nearly 300 patients approaching the end of their life last year, and involves 24 nurses.
To keep the scheme going, hundreds of thousands of pounds has to be generated over the next few years, and if fundraising goes well, it is hoped to expand the initiative in and around Edinburgh.
Around 75 per cent of terminally-ill people say they would like to die at home, rather than in a hospital or hospice, yet only a quarter of them do so.
Kate Stevenson, the nurse who is the face of the campaign, said it was her job to ensure that ratio improves.
She said: "It is a free service we provide so fundraising is really important to keep it going. We find the majority of patients want to be able to die at home, where they can be in familiar surroundings, look out at their garden and just have family members around.
"It is important not just for the patient, but the family too, so they can relax, talk, light candles, play music and even have a glass of wine. In a hospital setting, or even in a hospice, you couldn't expect that kind of thing."
The team works from 10pm until 7am, providing nursing and emotional support for patients through the night.
Now Marie Curie wants more people to access the service, with many who would qualify not aware it exists.
"People eventually come to us and say they wish they had known earlier," added Ms Stevenson.
"It isn't for everyone. Sometimes if there are young children around the family doesn't want the patient to die at home.
"But what is important is people get a choice."
The charity is appealing to people in the city to consider taking on fundraising activities to support the initiative.
Fiona Bushby, community fundraising manager, said: "It's about getting the appeal out there so people know about it.
"It's a great cause and helps us allow more people who wish to die at home the option to do so."
To get involved call 0131-470 2290 or visit www.mariecurie.org.uk/lothian.