The fundamental matrix is a basic tool in the analysis of scenes taken with two uncalibrated cameras. The 8-point algorithm and the improved 8-point algorithm are widely used linear methods for estimating the fundamental matrix. They have advantages of simplicity in implementation. But they are extremely sensitive to noise and outliers. Hence in most cases, they are useless virtually. A new robust linear method——weighted normalization algorithm is developed by introducing a cost function related to residual errors. Firstly, the matching points with a weight factor are normalized. Secondly, the eight parameters of fundamental matrix are calculated by using the 8-point algorithm. Experiments on simulated and real image data are conducted. The results show that this algorithm is very robust to noises and outliers, and the fundamental matrix with high accuracy can be found.