This paper presents a numerical approach for steady ship-wave problem, which is based on extension and modification of Dawson-type Rankine-source method in order to utilize arbitrary topology of free-surface panels. The wave radiation condition is numerically given, where 3rd-order upstream differential operator evaluates 2nd-derivative terms in the free-surface boundary condition. In this 1st report, the main emphasis is placed on application of O-type as well as conventional H-type topology free-surface panels. It appears that the former offers advantages over the latter due to the efficient panel distribution and improved resolution of the local-region bow-and shoulder-wave systems. The computational results are presented for Wigley and Series60 C_B=0.6 ship models including detailed comparisons with experimental data.