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To avoid the disadvantage of the globally identical learning rate in classical Gaussian Mixture Model (GMM), GMM is improved in this paper. The object movements are predicted by Kalman filter, and the learning rate is changed to a small value in the areas where the objects appear, which ensures the relative invariance of the background and make moving objects become clearer quickly. After the objects pass through, the learning rate is updated to a larger value to maintain the rapid response background variations. Some actual surveillance videos are processed with the proposed algorithm. The experimental results show that the presented approach can keep the effectiveness of foreground detection, and meanwhile suppress the noise of background. It implies that the improved GMM will perform better in moving object detection.