Orthogonal distance regression (ODR), a method of fitting a model to data in cases where observation errors in the independent variable cannot be neglected in regard to those in the dependent variables (and where the ordinary least squares approach is therefore inappropriate), involving minimization of the sum of squared orthogonal distances between each data point and the curve is described. An algorithm for solving the ODR problem, based on the trust region Levenberg-Marquardt algorithm, is suggested. Its global and local convergence is proved, and the computational effort per step is shown to be of the same order as the method for ordinary least squares. Three illustrative computational tests are given.