Eddy currents, which are induced in the magnet cryostat by pulsed magnetic field gradients in MRI, generate undesired eddy fields within the imaging volume. In this work, an automated and computerized algorithm to compensate these eddy currents is presented. The compensation is done in two steps: (i) Eddy fields are symmetrized electronically with an R-C filter. (ii) The symmetric eddy fields are compensated by another R-C filter. The compensation algorithm is iterative; therefore, errors that remain from one iteration are eliminated in the next iteration. Hence, the compensation process is very robust and accurate. It is shown that all the even harmonics of the eddy fields are eliminated by the symmetrization process, but the odd field harmonics remain. The amplitude of these odd harmonics can be significantly reduced if the gradient coils are designed so that the field they generate is spatially similar to the eddy fields.