An interplanetary autonomous navigation network, named the Internet of Spacecraft (IoS), is proposed in this paper to enable a Solar System-wide autonomous navigation capability for spacecraft. This network consists of two types of spacecraft, namely host and client spacecraft. The former provide the absolute reference for the whole network, and the latter determine their positions by communicating with the host spacecraft or other client spacecraft. To investigate the performance of IoS, a detailed application scheme that supports a flight from Earth to Mars is developed and analysed. IoS is not a simple extension of the navigation constellation. It is independent of the ground tracking system and the configuration of the network is flexible in that any spacecraft-installed identical device can be added to it. Moreover, client spacecraft whose positions have been determined can also be regarded as host spacecraft and provide further navigation information to others. This paper aims to provide technical support for future deep space exploration.