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Alternating stacks of metal and dielectric films with nano-hole arrays, called fishnet structures, control the propagation of electromagnetic waves. In such a structure, changing a dimension or a shape, especially the change in shape of nanoholes, affect propagation constants. In this study, we report the dispersivity of fishnet structures is controllable with different hole shapes, by measuring the interferometric fringe in various wavelengths. Two structures were fabricated, which consist of five alternating stacks of aluminum and silicon dioxide with nano-hole arrays. The holes in one of the structures are circular with diameters of 500nm, and the other are square with 500nm sides. The lattice constant in each case is 1,000nm. Since fishnet structures are wavelength-dependent structures, the variable-wavelength interferometric microscope was set up. The phase shift of the circular hole and the square hole fishnet were about 110 degrees and 85 degrees, respectively, within a tunable wavelength from 1,470nm to 1,545nm. These values were equivalent to a refractive-index-change of 0.8 and 0.6, respectively. From these results, fishnet structures indicate high dispersivity within target wavelengths. The dispersion of fishnet structure can be controlled by the shape of the hole.