A　boundary　element　method　for　three-dimensional　steady　ship　wave-making　potential　problems　is　established　with　the　Rankine　source　function　as　its　fundamental　solution.　In　the　treatment　of　the　linearized　free　surface　condition,　one-sided,　upstream　finite　difference　operator　(FDO)　is　used　to　suppress　the　upstream　waves,　and　the　equation　of　the　disturbance　velocity　is　established　so　that　the　first　order　FDO　can　be　used　in　place　of　the　second　order　FDO.　Compared　with　the　method　with　the　second　order　FDO,　the　current　method　gives　better　precision　and　stability.　Numerical　examples　are　presented　for　verification.