Quantum　memories　have　been　realized　in　different　physical　systems,　such　as　atomic　ensembles　or　solid　systems.　To　date,　all　quantum　memories　have　realized　the　storage　and　retrieval　of　photons　encoded　using　only　a　two-dimensional　space　spanned,　for　example,　by　the　orthogonal　polarization　states,　and　hence　can　only　store　a　quantum　bit.　Using　electromagnetically　induced　transparency　in　a　cold　atomic　ensemble,　we　report　the　experimental　realization　of　a　quantum　memory　storing　a　photon　encoded　in　a　three-dimensional　space　spanned　by　orbital　angular　momentum　(OAM)　states.　We　experimentally　reconstruct　the　storage　process　density　matrix　with　a　fidelity　of　85.3%　+/-　1.8%　using　a　4-f　imaging　system.　We　also　realize　storage　of　two　special　photonic　qutrit　states　as　examples.　Toward　storing　a　higher-dimensional　state　encoded　in　OAM　space,　the　efficiency　difference　between　different　OAM　states　should　be　considered　according　to　the　experimental　results.　The　capability　to　store　high-dimensional　quantum　states　with　high　fidelity　is　a　key　step　towards　building　high-dimensional　quantum　networks.