Accidents in marine operations are occurring consistently despite government safety initiatives and efforts to lower the number of accidents and the ensuing human casualties. Since each accident type has a different frequency and casualty rate, identifying risky accident types is important to determine the priority for taking necessary risk reduction actions. Usually, a risk is calculated using two criteria, i.e., the frequency and fatality of an accident. However, the accident statistics show that for the last 5 years from 2018 to 2022, the injury rate is more than three times the death rate in maritime accidents in Korean waters. Considering the importance of injury, unlike other previous studies, we perform a risk analysis with three criteria, i.e., frequency, death, and injury to complement the conventional risk calculation methods, which can help decision-makers allocate the limited resources to the riskiest types of accidents in order of priority. In doing so, we employed an integrated ordinal priority approach (OPA) and grey relational analysis (GRA) method to assign proper weight to each criterion and rank eight accident types. We categorized the accidents types into three different groups where safety accidents and collisions were ranked as the most dangerous types. The combined OPA and GRA technique has been effectively applied to other risky industries, as well as the maritime industry. Additionally, the proposed method is suitable for multi-criteria models when each criterion has a different importance. Finally, the method can be integrated into the framework of the risk ranking process to enhance the analysis results.