Quantum memory plays a pivotal role in the construction of quantum repeaters, which are essential devices for establishing long-distance quantum communications and large-scale quantum networks. To boost information capacity and signal processing speed, the implementation of high-efficiency multiplexed quantum memories is essential for the development of multiplexed quantum repeaters. In this work, we experimentally demonstrate an efficient multiplexed quantum memory by consolidating photons carrying high-dimensional orbital angular momentum (OAM) state from 4 individual channels into an elongated cold 87Rb atomic ensemble. Benefiting from the cold atomic ensemble with high optical depth, we obtain a storage efficiency exceeding 70% for the 4-channel multiplexed beam. The storage fidelities surpass 83% when all channels are operated in a 4-dimensional Hilbert space, which is far above the classical benchmark and validates the quantum functionality of our memory system. The achieved high-efficiency OAM multiplexed quantum memory opens up an avenue for efficient quantum information processing over multiple parallel channels, promising significant advances in the field of quantum communication and networking.