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We investigate bidirectional teleportation that works in a fair and efficient manner.Two explicit protocols are proposed to realize bidirectional teleportation with a controller.One is a symmetric protocol for two-qubit states.The other is an asymmetric protocol for single-and two-qubit states.We then devise a universal protocol for arbitrary n1-and n2-qubit states via a(2n1 + 2n2 + 1)-qubit entangled state,where n1 ≤ n2.The receiver only needs to perform the single-qubit recovery operation,which is derived by a general expression.Moreover,a(2n1 + 1)-bit classical communication cost can be saved within the controller\'s broadcast channel by the use of network coding technology.