This paper proposes a three-dimensional (3D) controlled quantum teleportation scheme for an unknown single-qutrit state.The scheme is first introduced in an ideal environment,and its detailed implementation is described via the transfor-mation of the quantum system.Four types of 3D-Pauli-like noise corresponding to Weyl operators are created by Kraus operators:trit-flip,t-phase-flip,trit-phase-flip,and t-depolarizing.Then,this scheme is analyzed in terms of four types of noisy channel with memory.For each type of noise,the average fidelity is calculated as a function of memory and noise parameters,which is afterwards compared with classical fidelity.The results demonstrate that for trit-flip and t-depolarizing noises,memory will increase the average fidelity regardless of the noise parameter.However,for t-phase-flip and trit-phase-flip noises,memory may become ineffective in increasing the average fidelity above a certain noise threshold.