CBTC(Communication Based Train Control) System can improve train operation efficiency by realizing moving block system which makes a continuous train interval control in accordance with the position and speed of train. Adopting radio transmission to make a continuous detection of train position and transmit the control data from the ground to a train, CBTC needs dedicated train operation and control algorithm which should be quite different from the conventional track-circuit-based train control system. This paper provides a train operation display and control algorithm for CBTC system in making train interval control, train route control and train supervision. Signalling pattern diagram is devised to analyze the train interval control mechanism of moving block system, and interlocking logic is devised to represent the train route control mechanism of moving block system. For train supervision, train occupation status on railway are displayed by using the segment which virtually divide the whole railway. The proposed method has been successfully applied to the development of CBTC system for the standardized AGT(automatic guided transit) which is under construction now in Korea, and also can be applied to any other CBTC system.