The 80-year-old was found at a house in Portadown on Wednesday afternoon.
A woman, who is also believed to be in her 80s, has been taken to hospital for treatment.
It is understood the man was discovered in the Levaghery Gardens area.
A Police Service of Northern Ireland spokeswoman confirmed officers are investigating the circumstances of the man’s death.
“Police are investigating the circumstances surrounding the sudden death of a man in his 80s at a house in Portadown this afternoon,” she said.
“A post mortem will be carried out in due course.
“A woman also believed to be in her 80s has been taken to hospital for treatment.”
DUP MLA Carla Lockhart said her thoughts are with the man’s family.
“Tragic news this evening in Portadown with the death of an elderly person and another one who has been taken to hospital,” she said.
“Our thoughts and prayers are with both this person and the family concerned.”
Ulster Unionist MLA Doug Beattie expressed his sadness.
“Sad news coming from Levaghery Gardens, Portadown,” he said.
“Emergency services are dealing with an incident which has resulted in one death and another being admitted to hospital.
“My thoughts are with the family and friends at this difficult time.”