In the paper we generalize the standard teleportation to the conclusive teleportation case which can teleportan arbitrary d-dimensional N-particle unknown state via the partially entangled quantum channel. We show that onlyif the quantum channel satisfies a constraint condition can the most general d-dimensional N-particle unknown state beperfect conclusively teleported. We also present a method for optimal conclusively teleportation of the N-particle statesand for constructing the joint POVM which can discern the quantum states on the sender's (Alice's) side. Two typicalexamples are given so that one can see how our method works.