A quantum memory for light is a key element for the realization of future quantum information networks. Requirements for a good quantum memory are versatility (allowing a wide range of inputs) and preservation of quantum information in a way unattainable with any classical memory device. Here we demonstrate such a quantum memory for continuous-variable entangled states, which play a fundamental role in quantum information processing. We store an extensive alphabet of two-mode 6.0 dB squeezed states obtained by varying the orientation of squeezing and the displacement of the states. The two components of the entangled state are stored in two room-temperature cells separated by 0.5 m, one for each mode, with a memory time of 1 ms. The true quantum character of the memory is rigorously proved by showing that the experimental memory fidelity 0.52±0.02 significantly exceeds the benchmark of 0.45 for the best possible classical memory for a range of displacements.