To estimate a relative pose for uncalibrated cameras with unknown distortion in multi-view 3D reconstruction, a robust method with high precision was proposed. Based on the epipolar geometry relationship, the radial fundamental matrix with unknown center of distortion is deduced. The weighted matrix is introduced into the coefficient matrix to control the correspondences using to estimate the radial fundamental matrix by singular value decomposition. Then the weighted matrix is updated according to the proposed criterion, and the calculation is performed iteratively. By comparing number of inliers and average distance to epipolar line, the optimal result of the radial fundamental matrix is obtained, determining whether to continue the iterative calculation. After iterative optimization, the final radial fundamental matrix can be used to estimate the center of distortion, distortion parameters and focal length. Experimental results show the efficiency, high precision and numerical stability of the proposed solution and when the mean variance of the noise is 2.5, the mean of distortion parameter error is less than 2% and the focal length estimation error is less than 3.5%.