A delay compensation algorithm is presented for a gaze-contingent video compression system (GCS) with a robust targeted gaze containment (TGC) performance. The TGC parameter allows varying compression levels of a gaze-contingent video stream by controlling its perceptual quality. The delay compensation model is based on the Kalman filter framework that models the human visual system with eye position and velocity data. The model predicts future eye position and constructs a high-quality coded region of interest (ROI) designed to contain a targeted number of gaze samples while reducing perceptual quality in the periphery of that region. Several model parameterization schemes were tested with 21 subjects using a delay range of 0.02 to 2 s and a TGC of 60 to 90%. The results indicate that the model was able to achieve TGC levels with compression of 1.4 to 2.3 times for TGC=90% and compression of 1.8 to 2.5 for TGC=60%. The lowest compression values were recorded for high delays, while the highest compression values were reported during small delays.