Quantum internet is an important basis for realizing multi-party quantum communication, distributed quantum computing, and other quantum information technologies. Quantum memory, as a significant part for realizing Internet, plays a pivotal role in the development and application of quantum information technology. Nowadays, the global optical fiber network has become a powerful carrier of information transmission, and quantum memory in communication band is highly valued because it is easy to be embedded in the current optical fiber network. Focus on telecom band optical quantum memory with rare earth ions doped solid-state system, the basic principle of rare earth ions doped solid-state quantum memory was firstly introduced, including rare earth doped material properties and memory protocol. the current state of the art was then introduced. Finally, a brief analysis on its future development trend was given, and the prospect for the construction of quantum Internet was made.