A systematic approach to passive shimming is proposed, and has been tested experimentally using a simultaneous gradient cancellation technique. In finding coil adjustments to correct gradients, the iterative application of the pseudoinverse (or generalized inverse) technique is used and a solution provided at each step. Each solution consists of a set of optimum values of adjustments. If the degree of freedom for adjustments is larger than the number of gradients to be corrected, the solution is the minimum norm solution. Through computer simulations, the algorithm is found to converge to a magnetic field homogeneous enough to allow nuclear‐magnetic‐resonance (NMR) imaging in only a few steps even in the presence of internal imperfections and misalignments as large as several 10 mm and an external asymmetric field affecting materials as near as a few meters. High homogeneity as well as fast convergence to a uniform magnetic field has been confirmed experimentally with the KAIS 1.5‐kG magnet. By use of the proposed algorithm, we have experimentally obtained a field homogeneity of a 1.5‐kG resistive magnet twice as homogeneous as that of the specified value with only a few iterations. Although it has been tested in the available low magnetic field, there are no restrictions in applying the technique to various magnets including superconductive magnets widely used in NMR imaging (in this case the algorithm is applied at the assembly stage).