Quantum memories that are capable of storing multiple spatial modes offer advantages in speed and robustness when incorporated into quantum networks. When it comes to spatial degrees of freedom, orbital angular momentum (OAM) modes have received widespread attention since they enable encoding with inherent infinite number of dimensions. Although the faithful storage of OAM qubits or qutrits has been realized in previous works, the achieved lifetimes are still on the order of a few microseconds as limited by the spatially dependent decoherence. We here demonstrate a long-lived quantum memory for OAM qutrits by suppressing the decoherence in the transverse and longitude direction simultaneously; the achieved fidelity beats the quantum-classical criteria after a storage time of 400 μs, which is 2 orders of magnitude longer than earlier works. The present work is promising for establishing high-dimensional quantum networks.