To avoid pollution of transportation applications, renewable energies are deployed. Whereas they are uncontrolled, fully controlled pollution-free energy sources and storage units should be also considered. However, a complicated direct current (DC) microgrid (MG) is obtained, which suffers from nonlinearities, high order, and uncertainties of the power elements. Therefore, it is vital to use advanced nonlinear controllers to assure closed-loop stability and performance of the overall system. In this paper, a neural network (NN)-based adaptive linear parameter varying (LPV) controller is suggested for the whole DC MG power system. The main advantage of the developed controller is that it deploys the operating information of all power energy sources to manipulate each component. This enhances the DC MG stability margin and fast regulation of the power and voltage. Besides, the proposed controller has a systematic and fully offline design algorithm by combining numerical solvers and theoretical theories. The LPV controller is designed via the numerical linear matrix inequality (LMI) approach and the adaptation law for the NN parameters is designed based on the Lyapunov stability theory. A DC MG benchmark including a 5kW fuel cell, a 5kW solar plant, and a 2kW battery package is considered as the case study, which can be utilized in future fully electric boats (EBs). Numerical simulations with different scenarios are conducted to verify the performance of the proposed controller. Furthermore, comparative results are provided to show the advantages of the proposed method dealing with power fluctuations of the solar plant and DC loads over state-of-the-art nonlinear methods.