She said hospice care wasn't just for people with cancer but also for those who had illnesses such as heart, liver or kidney failure, chronic respiratory disease and neurological conditions.
"As baby-boomers age and the number of people with serious chronic illnesses continues to rise, the demand for palliative care services also increases."
Some illnesses had a much more intensive demand on the service, she said.
She said the organisation's goal was to help alleviate patient suffering through high-quality pain and symptom management and to provide added support for the patients and their families.
"Unfortunately high quality palliative care does not come cheap and whilst we are grateful to the Government we rely on the community for financial support to cover the funding shortfall, which is over $700,000."
Ms Morgan said the hospice required more than $1.5 million a year to run.
"The shortfall is increasing by $100,000 a year. When I first started the gap was $400,000, now it's $700,000."
She said there was a good level of support out there, something which she put down to people knowing they eventually they were going to die and that everybody deserved a good, dignified death.
She said the telephone appeal operators wouldn't be asking for credit card details over the phone, but would instead be asking for pledges to donate. Those who are willing to would then be sent an invoice, she said.