A scheme for teleporting an unknown quantum state via a partially entangled particle pair is proposed. We show that teleportation can be successful realized with unit fidelity but less than unit probability if the sender performs a rotational operation on the teleported qubit and then performs computation basis measurements on the teleported particle and the half of the entangled particle pair respectively. The probability of successful teleportation is determined by both Schmidt coefficients of the entangled pair. This method can be generalized to the teleportation of an arbitrary and unknown multi-qubit state.