Isaiah May suffered severe brain injuries during his birth in 2009 at a hospital in Rocky Mountain House.
His parents, Rebecka and Isaac May, then spent months trying to prevent doctors from unhooking their son from a respirator in Edmonton.
After taking their fight to court, the couple were told there was no hope for the boy and he died in their arms in hospital in March, 2010.
The lawsuit statement of claim alleges the boy's death was untimely and caused by negligence.
Rosanna Saccomani, the family's lawyer, said the couple tried to reach a settlement with the hospital and were reluctant to file the lawsuit.
"It was a very difficult decision for the Mays to make. They went through a very, very long ordeal with the loss of their child," Saccomani said Friday.
"We have independent medical advice that there was a departure from the standard of care that they could have reasonably expected in the labour and delivery of Isaiah."
Statements of claim contain allegations that have not been proven in court.
The lawsuit says Rebecka May's pregnancy was healthy and uncomplicated.
She went to the hospital with contractions just before midnight on Oct. 23, 2009, and was told to return when they became more frequent.
The statement of claim says she returned to hospital a few hours later, where problems were noted about the fetal heart beat.
Rebecka May gave birth to Isaiah after 40 hours of labour. The boy was born with the umbilical cord wrapped several times around his neck. He was then sent by air ambulance to an Edmonton hospital where he was treated in the neonatal intensive care unit.
"The infant's condition did not improve in the following months and on the recommendation of neonatologists, life support was eventually terminated on March 11, 2010," reads the statement of claim.
The lawsuit alleges doctors and nurses failed to properly evaluate the infant's medical problems before he was born and failed to prepare for an emergency delivery by cesarean section.
The Mays are suing to recover funeral, accommodation, travel and parking costs as well for pain and suffering.
Thousands of people across Canada and around the world rallied behind the young couple's fight to keep their son on a respirator. Some right-to-life and religious groups in Canada and the United States also expressed their support.
A month after the baby died a University of Alberta nursing instructor called for a public inquiry into how the hospital in Rocky Mountain House handled the birth.
Prof. Donna Wilson said there should be an inquiry to see if anything at the hospital should have been done differently.
At the time Alberta Health Services said an internal inquiry was done into the circumstances of Isaiah's birth, but the results cannot be released due to patient confidentiality.