Quantum memories are essential for quantum information processing. Techniques have been developed for quantum memory based on atomic ensembles. The atomic memories through optical resonance usually suffer from the narrow-band limitation. The far off-resonant Raman process is a promising candidate for atomic memories due to broad bandwidths and high speeds. However, to date, the low memory efficiency remains an unsolved bottleneck. Here, we demonstrate a high-performance atomic Raman memory in 87Rb vapour with the development of an optimal control technique. A memory efficiency of above 82.0% for 6 ns~20 ns optical pulses is achieved. In particular, an unconditional fidelity of up to 98.0%, significantly exceeding the no-cloning limit, is obtained with the tomography reconstruction for a single-photon level coherent input. Our work marks an important advance of atomic memory towards practical applications in quantum information processing.