Paxton, whose career credits included roles in "Titanic," "Aliens," and HBO's "Big Love," died February 25, 2017, just days after undergoing heart surgery. He was 61.
Paxton's family alleges the surgeon used "a high risk and unconventional surgical approach with which he lacked experience" and that the hospital and surgeon, "misrepresented and/or concealed information relating to the risks of surgery," according to the suit.
They believe those factors contributed to Paxton's post-surgery complications.
"Bill Paxton and his family trusted the physicians and staff at this medical facility but instead Cedars-Sinai betrayed their trust," the family's attorney Bruce Broillet said in a statement. "The surgeon's actions resulted in this tragic and preventable death."
In a statement, Cedars-Sinai said state and federal privacy laws prohibit it from "commenting about patient care without written authorization." But, the statement added, "Nothing is more important to Cedars-Sinai than the health and safety of our patients."
"These remain our top priorities," the statement said. "One of the reasons for our high quality is that we thoroughly review concerns about any patient's medical care. This process ensures that we can continue to provide the highest quality care."
Paxton was survived by his two children, James and Lydia, and his wife of 30 years, Louise Paxton.
CNN's Stella Chan contributed to this story.