Waste Heat Recovery (WHR) marine systems represent a valid solution for the ship energy efficiency improvement, especially in Liquefied Natural Gas (LNG) propulsion applications. Compared to traditional diesel fuel oil, a better thermal power can be recovered from the exhaust gas produced by a LNG-fueled engine. Therefore, steam surplus production may be used to feed a turbogenerator in order to increase the ship electric energy availability without additional fuel consumption. However, a correct design procedure of the WHR steam plant is fundamental for proper feasibility analysis, and from this point of view, numerical simulation techniques can be a very powerful tool. In this work, the WHR steam plant modeling is presented paying attention to the simulation approach developed for the steam turbine and its governor dynamics. Starting from a nonlinear system representing the whole dynamic behavior, the turbogenerator model is linearized to carry out a proper synthesis analysis of the controller, in order to comply with specific performance requirements of the power grid. For the considered case study, simulation results confirm the validity of the developed approach, aimed to test the correct design of the whole system in proper working dynamic conditions.