Shimming is an important technique in development of nuclear magnetic resonance (NMR) magnets where image resolution is highly dependent on magnetic field homogeneity. Classically, shimming may be categorized into two types: 1) active shimming that incorporates with extra coils and precise tuning of their currents; and 2)passive shimming that incorporates with pieces of steel placed in a bore of a main magnet and their uniform magnetization under homogeneous external fields. Additional magnetic fields, produced by the coils and/or the steel sheets, compensate original magnetic field from the main magnet in such a way that the total field becomes more homogeneous. In this paper, we developed a passive shimming method based on linear programming optimization. Linear programming is well known to be highly efficient to find a global minimum in various linear problems. We firstly confirmed the linearity of magnetization of ferromagnetic pieces under a presence of external magnetic fields. Then, we adopted the linear programming to find optimized allocation of the steel pieces in the inner bore of a main magnet to improve field homogeneity.