A quantum memory with a high storage efficiency and a long coherence time is an essential element in quantum information applications. Here, we report our recent development of an optical quantum memory with a rubidium-87 cold atom ensemble. By increasing the optical depth of the medium, we have achieved a storage efficiency of 65% and a coherence time of 51 μs for a weak laser pulse. The result of a numerical analysis based on the Maxwell-Bloch equations agrees well with the experimental results. Our result paves the way toward an efficient optical quantum memory and may find applications in photonic quantum information processing.