In this paper, we explicitly present a general scheme for controlled quantum teleportation of an arbitrary multi-qudit state with unit fidelity and non-unit successful probability using d-dimensional nonmaximally entangled GHZ states as the quantum channel and generalized d-dimensional Bell states as the measurement basis. The expression of successful probability for controlled teleportation is present depending on the degree of entanglement matching between the quantum channel and the generalized Bell states. And the formulae for the selection of operations performed by the receiver are given according to the results measured by the sender and the controller.