Inspectors found problems with the way Queen Elizabeth Hospital in Birmingham runs its heart unit after a high death rates compared with other hopsitals.
The trust ignored repeated warnings over high death rates, the report said.
The trust said patient safety remained its "number one priority".
University Hospitals Birmingham NHS Foundation Trust has now been ordered to make improvements and send weekly surgery results to the Care Quality Commission (CQC).
Read more news for Birmingham
The report said the trust has only recently started a quality improvement programme (QIP), despite concerns being identified in 2013 and consultants approaching the executive team in 2014 with concerns around patient deaths and outcomes.
The trust was also informed that its death rates were outside the national average in March last year.
England's chief inspector of hospitals, Prof Sir Mike Richards, said: "Initial data regarding surgery outcomes in the months since our inspection show an improvement but we need to continue to monitor the service."
Data from the Society for Cardiothoracic Surgeons showed the cardiac surgical unit at Queen Elizabeth Hospital had an above average death rate over the three years from April 2011 to March 2014.
A spokeswoman for University Hospitals Birmingham NHS Foundation Trust said on Tuesday: "None of the cardiac surgeons currently working at UHB are outliers for mortality outcomes and we are confident they will continue to offer the highest standards of care and expertise in delivering their service.
"The trust established a QIP for the cardiac surgery service in July 2015, which is ongoing and subject to external review.
"At the time of the CQC inspection in December 2015, the QIP had already improved outcomes and internal issues within the service.
"The subsequent report has added awareness and pace to what is considered a valuable exercise to enhance both staff and, more importantly, patient benefit."
A culture of bullying prevented staff at an NHS trust from speaking out about the number of heart surgery patients who were dying, a report has found.