Background modeling and motion detection is the one of the most significant real time video processing technique. Until now, many researches are conducted into the topic but it still needs much time for robustness. It is more important when other algorithms are used together such as object tracking, classification or behavior understanding. In this paper, we propose efficient multi-modal background modeling methods which can be understood as simplified learning method of Gaussian mixture model. We present its validity using numerical methods and experimentally show detecting performance.