The virus, often referred to as the winter vomiting bug, caused "severe disruption" between September 2017 and March 2018, the Mid Yorkshire NHS Hospitals Trust said.
The illness causes sickness and diarrhoea and in some cases, a high temperature and aching limbs.
While most people recover from their symptoms within a couple of days, it is highly contagious and can be dangerous for vulnerable groups, such as the very young and the very old.
There were eight separate outbreaks of the norovirus at Pinderfields between September 1 and March 27, papers from the trust confirmed.
The worst of these occurred in the hospital's stroke and neurology unit, which affected 22 patients and 13 staff.
The outbreak was first reported on December 30 and lasted for a full four weeks.
However, the scale of the problem was much greater at Dewsbury Hospital, which is also run by the trust.
More than 300 patients went down with the norovirus between April 2017 and March 2018.
A report on the issue, which will go before the trust board this week said: "The virus is usually mild, self-limiting and most people recover in one to two days.
"Most people make a full recovery within a couple of days but it can be dangerous for the very young and elderly people.
"It is important to keep patients hydrated, particularly the very young and elderly. Hand washing is a vital measure in reducing the risk of transmission."
"The trust and in particular Dewsbury Hospital experienced severe disruption due to outbreaks of the winter vomiting virus. A large number of bed days were lost due to the closures of wards."
Dawn Parkes, the trust's deputy director of nursing and quality, said staff would be doing all they could to prevent outbreaks during the winter ahead.
She said: "As in previous years we are reminding everyone about the importance of washing their hands regularly with soap and water.
"It is the single biggest step everyone can take to reduce the risk of infection.
"We are also keeping on top of our supplies to ensure we have sufficient stocks of the right protective equipment and testing kits, in order that we can appropriately manage those patients who do present with or develop norovirus symptoms.”