The paper presents an application of ship design optimisation subject to epistemic uncertainty. Generally, uncertainty that results from intrinsic variability (e.g. stochastic environmental or operating conditions) is termed aleatoric. Conversely, uncertainty is described as epistemic when it results from a lack of knowledge about a quantity whose true value (continuous or discrete) exhibits no actual variability (e.g. lack of information in the current stage of the design). Following a Bayesian approach, all the uncertainties are assigned a probability density function (PDF). Specifically, quantities with aleatoric uncertainty may be modelled as random variables through constructing their PDFs from observed data. Conversely, parameters with epistemic uncertainty may be assigned a PDF and the probability is inherently the degree of belief in a proposition. The present work addresses the epistemic uncertainty related to the location of the ship centre of gravity (CG), when optimising the hull form. Following a Bayesian approach, a probability density function (PDF) of the CG location is defined. Two complimentary formulations are presented and applied to the hull form optimisation.