Abstract Predictive display is a promising approach to tackle large time delays that greatly degrade the performance of teleoperation systems. Most of the existing predictive display schemes assume that observations of the current system states can be obtained directly or be estimated based on measurements with a single time-delay and single frequence, and then the future system states can be predicted by propagating the current states forward a round-trip transmission cycle. However, in actual applications the current states often have to be estimated based on multi-time-delay multi-rate measurements. To make full use of delayed measurements and improve the prediction accuracy, a novel predictive display algorithm is proposed to deal with multi-time-delay multi-rate measurements and missing data. Firstly, through ‘moving’ some of the delays in downlinks to the uplink the predictive display problem is converted into a standard filter problem and a prediction problem, which can be tackled by an observer-predictor structure; then the re-organized innovation analysis is utilized and extended in the observer to deal with multi-time-delay multi-rate measurements as well as missing data with the help of indication functions. Finally simulation results show the effectiveness of our novel predictive display algorithm.