In this paper, we propose a real-time communication scheme that can be used in general point-to-point real-time multicomputer systems with wormhole switching. Real-time communication should satisfy the two requirements of predictability and priority handling. Since traditional wormhole switching does not support priority handling, which is essential in real-time computing, flit-level preemption is adopted in our wormhole switching. Also, we develop an algorithm to determine the message transmission delay upper bound to predict worst-case message delay. Simulation results show that the delay upper bounds calculated using the proposed algorithm are very close to actual average message transmission delays for messages with high priorities.