With extensive number of power electronically interfaced loads and generations, ship microgrids exhibit similar traits as terrestrial microgrids. The replacement of conventional power transformers with smart transformers in ship microgrid adds flexibility to the system. However, the presence of large number of smart power converters in the ship power systems introduce power quality problems, voltage and frequency violations, etc. Moreover, large dynamic loads in ships augment the challenges for ship power operators. This necessitates a proper control and power management strategy for a ship microgrid. This paper presents a power management strategy for a diesel generator driven smart transformer based ship microgrid. The proposed power management strategy aims to reduce the power drawn from diesel generator by minimizing the LVAC bus power, while maintaining the bus voltages within desired limits. Simulation results validate the effectiveness of the proposed strategy.