The multipole fields are widely used in electron-optical devices and instruments. The multipole fields are generated by several azimuthaly-arranged electrodes or pole-pieces and, are thereby not rotational symmetric. They generally possess some planes of symmetry or anti-symmetry.The Fourier-transform method is used to decompose the three dimensional potential distribution into a series of independent two dimensional potentials, which can be calculated easily by the relaxation method. For this purpose, the three dimensional boundary values must be expressed in Fourier-series with respect to the azimuth θ in eylindrical coordinates. After these treatments, the corresponding two dimensional potentials can be calculated and superimposed.A computer program has been worked out for calculation of the properties of the multipole fields and its fringe fields. Some examples of importance such as quadrupole lens or doublet, and a toroidal deflection coil have been treated in detail. The numerieal results show that the Fourier-transform method for multipole field is a useful means for analysis and design of electron-optical devices.