Entanglement between a photon and an atomic memory is an important tool for quantum repeater research. By using the Duan-Lukin-Cirac-Zoller (DLCZ) process in the atomic ensemble, quantum entanglement between a photon and an atomic spin-wave memory is produced. With the further development of quantum information, it is necessary to put forward higher requirements for the diversity and controllability of quantum memory. In this work, we experimentally demonstrate an optical memory in cold atomic ensemble with enhanced fiber-cavity and high-fidelity optical memory for the first time. We design a fiber cavity to enhance the coupling strength between light and atomic ensemble and then improve the optical retrieval efficiency. Unfortunately, the use of fiber cavity may lead to the decrease of fidelity. Therefore, it is vital to realize high fidelity in the enhanced fiber-cavity optical memory. The cavity has a round-trip length of 1.5 m and a free spectral range of 190 MHz. The finesse (F) of the cavity with the cold atoms in the DLCZ condition is measured to be \sim 18. In cavity-enhanced DLCZ scheme, we use a fiber cavity instead of a stationary cavity. If a stationary cavity is used, the signal light will be reflected by the end mirror of the cavity and then pass back through the atoms. The storage of the backward signal light will generate a short-wavelength spin wave and then lead to a rapid decoherence of the memory. When cavity is locked by using the PDH frequency locking technique, we observe that the production probability of the Stokes photons is increased by 4.6 times higher than that without cavity and retrieval efficiency of atomic spin wave is increased by 1.6 times that without cavity due to the optical cavity enhancement effect. The presented cavity-enhanced storage shows that the retrieval efficiency is \sim 22%, corresponding to an intrinsic retrieval efficiency of \sim 40%, at the same time the fidelity of the quantum state is \sim 92%. The accomplishment of this project will provide another effective way of realizing long-distance quantum communication and large-scale quantum network construction.