A B-spline based higher order panel method (hereinafter, HiPan) is developed for the motion of bodies in ideal fluid, either of infinite extent or with free boundary surface. In this method, both the geometry and the potential are represented by B-splines, and it guarantees more accurate results than most potential based panel methods. In the present work, we apply the HiPan, which differs with the works at MIT in evaluating the induction integrals, to two major marine hydrodynamic problems: analysis of propulsive performance of the marine propellers and the motion of the floating bodies on the free surface. The present HiPan is shown superior to the constant panel method (hereinafter, CoPan) in predicting flow quantities in the area of the thin trailing edge and blade tip of the propeller. Numerical results are validated by comparison with experimental measurements.