Risk assessment is an essential exercise for process systems from early conceptual design to operation and subsequently during decommissioning. Risk assessment methods have evolved over the past two decades from index-based methods to detailed quantitative methods. The Bayesian network (BN) is a recent developed technique used for risk assessment that utilizes updating, adapting and discrete-time-based analysis properties. Although the BN is a powerful technique, it continues to face the challenge of modelling non-linear complex correlations of process components. This paper proposes a copula-based Bayesian network model that assists in overcoming the challenge of non-linear relationships. In addition to defining conditional probabilities, the copulas are also used to describe the joint probability densities of the network nodes in the BN. Application of the proposed model is demonstrated using a process accident case study. The results reveal that the proposed model is effective in estimating more reliable accident probabilities. A sensitivity analysis is also conducted to identify important factors that need to be monitored to prevent accident occurrence. Moreover, the focus of the present study is on process systems. However, the proposed model is applicable to most engineering systems. (C) 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.