One potential application of image-guided radiotherapy is to track the target motion in real time, then deliver adaptive treatment to a dynamic target by dMLC tracking or respiratory gating. However, the existence of a finite time delay (or a system latency) between the image acquisition and the response of the treatment system to a change in tumour position implies that some kind of predictive ability should be included in the real-time dynamic target treatment. If diagnostic x-ray imaging is used for the tracking, the dose given over a whole image-guided radiotherapy course can be significant. Therefore, the x-ray beam used for motion tracking should be triggered at a relatively slow pulse frequency, and an interpolation between predictions can be used to provide a fast tracking rate. This study evaluates the performance of an autoregressive-moving average (ARMA) model based prediction algorithm for reducing tumour localization error due to system latency and slow imaging rate. For this study, we use 3D motion data from ten lung tumour cases where the peak-to-peak motion is greater than 8 mm. Some strongly irregular traces with variation in amplitude and phase were included. To evaluate the prediction accuracy, the standard deviations between predicted and actual motion position are computed for three system latencies (0.1, 0.2 and 0.4 s) at several imaging rates (1.25–10 Hz), and compared against the situation of no prediction. The simulation results indicate that the implementation of the prediction algorithm in real-time target tracking can improve the localization precision for all latencies and imaging rates evaluated. From a common initial setting of model parameters, the predictor can quickly provide an accurate prediction of the position after collecting 20 initial data points. In this retrospective analysis, we calculate the standard deviation of the predicted position from the twentieth position data to the end of the session at 0.1 s interval. For both regular and irregular lung tumour motions, with prediction the range of average errors is 0.4–2.5 mm in the SI direction from shorter to longer latency, corresponding to a range of 0.8–4.3 mm without prediction; for the AP direction a range of 0.3–1.6 mm is obtained with prediction, corresponding to a range of 0.6–3.0 mm without prediction. For 0.2 s and 0.4 s system latency, with prediction the localization based on a relatively slow imaging rate (2.5 Hz) can achieve a better or similar precision compared with no prediction but on a fast imaging rate (10 Hz). This means that precise localization can be realized at a slow imaging rate. This is important for the application of kV x-ray imaging systems and EPID-based systems in image-guided radiotherapy. In conclusion, the adaptive predictor can successfully predict irregular respiratory motion, and the adaptive prediction of respiration motion can effectively improve the delivery precision of real-time motion compensation radiotherapy.