The intersection problem of three-dimensional free form surfaces can be solved by geometrical and numerical methods. Up to now, the subdivision technique, which is classified under the former, has been largely employed to find the cross section of ship hull form. In this paper, an algorithm is presented for intersecting ship hull form in high speed. The high speed calculation algorithm is based on simple numerical methods, such as the secant method, false position method and bisection method. The algorithm is directly applicable to depicting arbitrary ship cross sections, drawing ship lines and constructing the offset table.