In this paper, we propose a new method to estimate the FOE (Focus of Expansion) from moving camera image sequence for vehicle motion understanding, which does not rely on optical flow vectors. Motion understanding of the camera is very important in many applications. Most of the conventional methods for detection and estimation of the position of FOE rely on estimation of optical flow vector in the input image sequence. However, errors in estimating optical flow vector result in inaccurate estimation of FOE. In our method, we synthesize the input image and create an expected image of the next frame by using optical flow vectors. Optical flow vectors are obtained from the hypothesis of position of FOE and global constraint of optical flow. We evaluate the position of FOE by SAD (Sum of Absolute Differences) value between the warped and the real image. The proposed method estimates the position of FOE by minimizing SAD. For demonstrating the efficacy of the proposed method, we apply the proposed FOE estimation method for detecting lateral position of a vehicle. The experimental results show advanced performance comparing with FOE estimation based on a commercial optical flow vector field estimating software.