We theoretically investigate the optical memory in a nanofiber system via electromagnetically induced transparency (EIT) in a nonlinear region. Because of the tight transverse confinement, the light-atom interaction is significantly enhanced and thus, the EIT effect is enhanced. The inhomogeneous mode field distribution contributes spatially to the EIT dispersion. We develop a systematic analysis method to study the nonlinearity of the system and prove that the optical soliton is available in the system and can be stored and retrieved with high efficiency and stability. We also study a strategy to optimize the soliton optical memory. The results obtained in this study are promising for practical applications of all-optical information processing.