The concept of energy based Lyapunov control is extended to marine vessels with a nonsymmetric system inertia matrix. Acceleration feedback is used as the main tool to symmetrize the nonsymmetric part of the system inertia matrix. The main reason for a nonsymmetric mass distribution is hydrodynamic added mass which depend on the forward speed of the vessel and the frequency of the incoming waves. This is a well known phenomenon for marine vessels moving at positive speed in waves while low-speed applications like dynamic positioning systems are fairly well described with a symmetric system inertia matrix. The main contribution of the paper is a new Lyapunov-based design technique incorporating acceleration feedback to shape the kinetic energy of the system. Acceleration feedback is implemented in conjuncture with a nonlinear PID-controller derived from vectorial backstepping. The result is a uniformly globally asymptotically stable (UGAS) closed-loop control system applicable to marine vessels with nonsymmetric system inertia matrices. Typical applications are ships in maneuvering situations, vessels in transit and high speed craft where nonsymmetric added mass effects must be compensated for.