The Hospice of the Valleys, located in Tredegar, hopes to open the new building in 2010, provided all the money is raised.
The facility will accommodate the more than 20-person staff currently dealing with cramped conditions, walesonline.co.uk reports.
Andrew Richards, chief executive of Hospice of the Valleys, said the hospice had grown "massively in the last few years" and that new elements are needed to enhance their services. Individual clinic rooms are essential for dignity and confidentiality when patients meet staff and therapists," Richards told the website.
The appeal to raise the funds has already yielded £350,000 and is being called Precious Moments. The name comes from "helping people come to terms with their illness and releasing them from fear so they can focus on those things which are precious in their lives," according to the Hospice website.
In the UK, the government contributes an average of 31 percent of running costs for adult hospices. The rest of the money comes from fundraising.
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