Cross-ratio (CR) based methods offer many attractive properties for remote gaze estimation using a single camera in an uncalibrated setup by exploiting invariance of a plane projectivity. Unfortunately, due to several simplification assumptions, the performance of CR-based eye gaze trackers decays significantly as the subject moves away from the calibration position. In this paper, we introduce an adaptive homography mapping for achieving gaze prediction with higher accuracy at the calibration position and more robustness under head movements. This is achieved with a learning-based method for compensating both spatially-varying gaze errors and head pose dependent errors simultaneously in a unified framework. The model of adaptive homography is trained offline using simulated data, saving a tremendous amount of time in data collection. We validate the effectiveness of the proposed approach using both simulated and real data from a physical setup. We show that our method compares favorably against other state-of-the-art CR based methods.