The maritime transport industry is increasingly reliant on computing and communication technologies, and the need for cyber risk management of critical systems and assets on vessels is becoming critically important. In this paper, a comprehensive cyber risk assessment of a ship is presented. An experimental process consisting of assessment preparation activities, assessment conduct and results communication has been developed. The assessment conduct relies on a survey developed and performed by interviewing a ship's crew. Computational vulnerability scanning of the ship's Electronic Chart Display and Information System (ECDIS) is introduced as a specific part of this cyber security assessment. The assessment process presented has been experimentally tested by evaluating the cyber security level of Kobe University's training ship Fukae-maru. For computational vulnerability scanning, an industry-leading software tool has been used, and a quantitative cyber risk analysis has been conducted to evaluate cyber risks on the ship.