Devon Primary Care Trust is in the top 10 most complained about NHS bodies, according to a report by the Health Service Ombudsman.
The trust had 84 complaints, mostly about dentistry, from 2009 to 2010 - the 10th highest number in England.
It is the first time information about how many complaints are made to the ombudsman has been made public.
The trust said as one of the largest PCTs in the country it would expect to receive a high number of complaints.
'Failing to listen'
Vanessa James, NHS Devon director of corporate affairs, said: "Of the 84 complaints to the ombudsman only four were investigated, of which two were partially upheld.
"We are pleased that patients feel able to contact our complaints department easily and we know the majority are happy with the resolution."
Devon PCT manages community hospitals and health centres in the county.
Altogether, 270 complaints were made about NHS bodies in Devon and Cornwall.
Plymouth Hospitals NHS Trust, which runs the city's Derriford hospital, had 64 complaints.
The trust said five were being investigated and the remainder had either been referred back for further local resolution or the Ombudsman had found that the trust had done everything possible to try and resolve the complaint.
Cornwall and Isles of Scilly PCT had 45 complaints with one fully upheld and the Royal Cornwall Hospitals Trust 36.
The Royal Devon and Exeter NHS Foundation Trust had 30 complaints.
In her report Listening and Learning the Health Service Ombudsman Ann Abraham warned that the NHS was missing "a rich source of free information about patients" by failing to listen and learn from complaints.