A B-spline panel method is developed to solve a boundary integral equation for three-dimensional potential flow problems. In particular, a nonuniform rational B-spline (NURBS) surface is introduced to accommodate a precise geometric description of a given body. For the unknown (potential) description over the surface, uniform B-spline basis functions are used. A collocation approach is adopted for numerical computations, and influence coefficients are evaluated in a robust manner over the surface defined by NURBS. Convergence characteristics of the present method have been investigated in the numerical experiments on the unbounded problem of a sphere, the radiation problem of a floating hemisphere, and the diffraction problem of a submerged spheroid. It is shown that the numerical results are in excellent agreement with analytical solutions in all cases considered. It is concluded that the NURBS panel method is superior to existing panel methods in geometric description of body surface, and convergent solutions can be achieved rapidly with a small number of panels.