Background: Healthcare statistics, issued by various international organizations, show that medical errors in health centers impose high costs on patients and hospitals and increase the rates of morbidity and mortality around the world. Due to the potential risks of cardiovascular diseases, the occurrence of any errors can potentially endanger the patients’ lives and incur costs on them, as well as hospitals. On the other hand, anesthesia is one of the priorities for risk management in clinical care. Objectives: This study aimed to identify, classify, and evaluate anesthesia failures in open heart surgeries, using the healthcare failure mode and effects analysis (HFMEA) technique. Methods: The anesthesia process in open heart surgery was reviewed using the HFMEA technique, and four processes, 25 sub-processes, 95 activities, and 204 risks were extracted. The causes of failure were also identified, and four failure modes were determined as the most important failures, based on the qualitative and quantitative methods; finally, some solutions were proposed. Changes in the level of healthcare workers’ knowledge and competence, computer use and timing, and the amount of administered medications were identified as the potential risk factors and errors. Results: The inadequate awareness and knowledge of healthcare workers, non-use of computers, prescription errors, technique errors, and timing and amount of medication administration were identified as the errors and risk factors. Based on the present findings, another expert needs to evaluate the design, feasibility, and prioritization of techniques, including continuing medical education for anesthesia professionals and experts, statutory documentation, and control of the individuals’ activities. Conclusions: Based on the present findings, establishing a risk management committee seems essential to identify errors and improve the design and plan of different techniques so as to execute, monitor, control, and review errors in a cycle of continuous improvement.