We adopted a combination of pieces of permanent magnets and a single-channel (SC) shim coil to shim the magnetic field in a magnetic resonance imaging system dedicated for skeletal age assessment of children. The target magnet was a 0.3-T open and compact permanent magnet tailored to the hand imaging of young children. The homogeneity of the magnetic field was first improved by shimming using pieces of permanent magnets. The residual local inhomogeneity was then compensated for by shimming using the SC shim coil. The effectiveness of the shimming was measured by imaging the left hands of human subjects and evaluating the image quality. The magnetic resonance images for the child subject clearly visualized anatomical structures of all bones necessary for skeletal age assessment, demonstrating the usefulness of combined shimming.