Graham is calling on NHS chiefs to find a solution and allow Kilbryde hospice to finally offer round the clock palliative care.
He Graham met hospice vice-chairman Gordon McHugh last week to raise concerns at the length of time it has taken to open up their 12 beds to patients.
Despite the building opening more than two years ago not a single patient has stayed there overnight.
The hospice is waiting for NHS Lanarkshire to complete a review into palliative care.
Graham said: “I was pleased to visit, having seen the building take shape and then open but sad to see facilities which have effectively been mothballed ever since.
“It is actually wrong to call it a hospice at the moment because they can’t offer the end of life service that a hospice does.
“People in East Kilbride raised £4million to build this wonderful facility and we deserve to see it being fully operational.
“I have written to NHS Lanarkshire chief executive Calum Campbell asking when a decision will be made and stressing the need for palliative care to be offered in Lanarkshire’s largest town.”
Mr Simpson visited the hospice after being contacted by constituents concerned that it is not open 24 hours a day.
He saw a hair salon there which was kitted out by top stylist Taylor Ferguson, as well as high-tech baths which can help to alleviate pain.
Graham said: “Gordon and the team have done a great job so far but they could be doing so much more and I hope they get the go ahead.
“It’s imperative that we make Kilbryde a truly supportive 24 hour hospice as soon as possible so all of these excellent facilities can be used by the people who need them most.”