A new technique to correct non-linear distortion of endoscopic images based on L2-norm approximation is proposed. A mathematical model is defined that maps the endoscopic images from the distorted image plane onto an undistorted image plane. A set of model parameters is defined, consisting of the image distortion centre, corrected centre and expansion polynomial coefficients representing radial distortion correction. A new method to find the image distortion centre based on a curvature criterion is also developed. The expansion coefficients are estimated on the basis of the degree of straightness of the grid lines in an image of a test grid consisting of dots in a rectangular pattern. The corrected image centre is computed by ensuring that the distances between neighbouring test dots of different grid lines in the corrected image are the same. The quantitative data providing the results and errors of the expansion characteristics are presented. The performance of the proposed distortion correction algorithm is validated with grid patterns of different orientations. The algorithm is also applied to typical endoscopic images, and the results are presented. The high-speed response of the proposed technique is a key step towards on-line camera calibration.