Recently, a new class of $W$-states has been defined by Agarwal and Pati cite{agarwal} and it has been shown that they can be used as a quantum channel for teleportation and superdense coding. In this work, we identify those three-qubit states from the set of the new class of $W$-states which are most efficient or suitable for quantum teleportation. We show that with some probability $|W_1>=(1/2)(|100>+|010>+sqrt{2}|001>)$ is best suited for teleportation channel in the sense that it does not depend on the input state.
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