The radiation problem for oscillating bodies on the free surface has been formulated by the over-determined Green integral equation, where the boundary condition on the free surface is satisfied by adopting the Kelvintype Green function and the irregular frequencies are removed by placing additional control points on the free surface surrounded by the body. The B-Spline based higher order panel method is then applied to solve the problem numerically. Because both the body geometry and the potential on the body surface are represented by the B-Splines, that is in polynomials of space parameters, the unknown potential can be determined accurately to the order desired above the constant value. In addition, the potential expressed in B-Spline can be differentiated analytically to get the velocity on the surface without introducing any numerical error. Sample computations are performed for a semi spherical body floating on the free surface for six-degrees of freedom motion. The added mass and damping coefficients are compared with those by the already-validated constant panel method of the same formulation showing strikingly good agreements.