We have investigated regional Variations of elastic properties using magnetic force-controlled atomic force microscopy (AFM). A piece of small magnet was fixed at the end of the backside of the AFM cantilever so as to apply forces directly to the tip through the external magnetic field of a coil. When the forces applied to the tip are modulated with direct force modulation. and the resulting amplitude of oscillation is measured, a sensitive measurement of the local contact stiffness can be made. We have applied this technique to polymer films of poly(ethylene oxide) (PEO) on mica. The soft PEO was measured easily with the faint magnetic forces between the tip and sample. The contrast of the image can selectively be enhanced on the basis of the local elasticity difference, when a soft cantilever was used. On the contrary the spring constant of the cantilever which we should use is determined by the elasticity of materials using indirect force modulation by modulating the sample displacement. The direct force modulation technique is a convenient method to investigate, especially, the elasticity of unknown materials on the nanometer scale.