The　functional　k-means　problem　involves　different　data　from　k-means　problem,　where　the　functional　data　is　a　kind　of　dynamic　data　and　is　generated　by　continuous　processes.　By　defining　a　new　distance　with　derivative　information,　the　functional　k-means　clustering　algorithm　can　be　used　well　for　functional　k-means　problem.　In　this　paper,　we　mainly　investigate　the　seeding　algorithm　for　functional　k-means　problem　and　show　that　the　performance　guarantee　is　obtained　as　8(ln　k　+　2).　Moreover,　we　present　the　numerical　experiment　showing　the　validity　of　this　algorithm,　comparing　to　the　functional　k-means　clustering　algorithm.