A new technique for calibrating a camera with high accuracy and low computational cost is proposed. The geometric camera parameters considered include camera position, orientation, focal length, radial lens distortion, pixel size, and optical axis piercing point. With this method, the camera parameters to be estimated are divided into two parts: the radial lens distortion coefficient κ and a composite parameter vector c composed of all the above-mentioned geometric camera parameters other than κ. Instead of using nonlinear optimization techniques, the estimation of κ is transformed into an eigenvalue problem of an 8 x 8 matrix. The method is fast because it requires only linear computation; it is accurate because the effect of the lens distortion is considered and because all the information contained in the calibration points is used. Computer simulations and real experiments show that the calibration method can achieve an accuracy of 1 part in 10,000 in 3-D measurement, which is better than that of the well-known method proposed by R. Y. Tsai.