The TMO (Time-triggered Message-triggered Object) model is a well-known real-time object model for distributed and timeliness-guaranteed computing. A distributed environment of the model may be configured by a number of the TMO nodes as a private network. It requires high reliability due to the feature of a distributed IPC message. The TCP seems to be suitable to this model. However, if a message needs to be broadcasted or multicasted to the other objects, the more the number of the nodes increases, the less efficient the repetitive unicast delivery of the message is. A multicast transport protocol can be considered to overcome this problem. In this paper, we propose a reliable multicast transport protocol suitable for supporting a distributed environment of the TMO model and discuss its performance with respects to the real-time delivery and throughput comparing with the alternative protocols. Results from the extensive performance measurement demonstrate that the proposed protocol outperforms the conventional TCP and existing RMT protocols.