In recent years, the size (weight and volume) of cruise ships are experiencing spectacular increase, coherently with the increase in energy consumption and carbon emissions. However, the regulations about pollutant emissions imposed by the International Maritime Organization are becoming more and more strict. In order to face up to this issue, the energy system of cruise ships is constantly being modified. In this paper, the structure of the cruise ship's energy system with multiple facilities such as an internal combustion engine, gas turbine, dual fuel engine, PV panels, and the wind turbine is pre-established. Then, a multi-objective mathematical programming model is formulated to determine the selection and capacity of facilities with minimal total annual cost and size, while the emissions, energy balance and technical constraints are taken into account. By adopting the augmented ε-constraint method, the design and operation strategies could be obtained. As an illustrated example, the model is applied to a real cruise ship, and the Pareto frontier could provide ship designers with well-balanced solutions based on economic and size priorities, and with the increase in the proportion of size objective, the total annual cost increases and size decreases gradually. Compared with the reference energy system, the optimal energy system could reduce the total annual cost by 12.6% if only the economic objective is considered and reduce the size by 21.1% if only the size objective is considered. In multi-objective condition, the CO, NOx, and SOx emissions could be reduced by 29.1%–61.3%, 42.8%–61.3%, and 42.8%–61.3% per year, respectively. Moreover, a sensitivity analysis is conducted, and the result shows that the size and consumption cost of Marine Gas Oil (MGO) and Liquefied Natural Gas (LNG) are more sensitive to the change of the proportion of size objective compared to Heavy fuel oil (HFO) and Marine diesel oil (MDO).