Qutrit is the natural extension of qubit in quantum information processing and has quite a few advantages that outperform qubit.In this paper,we investigate the feasibility of teleportation of an unknown qubit state,as well as an unknown qutrit state using a two-qutrit entangled pair.We show that by carefully constructing the measurement bases,both the qubit and the qutrit can be faithfully teleported from Alice to Bob with a two-qutrit maximally entangled state.