Due to emission regulations, the ship is sometimes restricted or even prohibited to use diesel when berthing in port, and the shore power (called the "cold-ironing") takes part as power supplier. For a green ship with onboard photovoltaic (PV) systems, energy management for maritime PV/battery/diesel/coldironing hybrid energy system (HES) can significantly reduce the electricity cost of a ship. In this paper, the optimal operation of HES on a ship is modelled as an optimization problem subject to a number of constraints, including emission regulations of ports. Optimal control and model predictive control (MPC) methods are developed to dispatch the power flow when the ship is in port. Finally, the proposed approaches are tested by simulation experiments for different cases of cold-ironing service prices and emission regulations. Experimental results show that the optimal operation of maritime HES can bring promising electricity cost savings and robustness. (C) 2018 Elsevier Ltd. All rights reserved.