Based on the theory of Fourier-transform synthesis method, a minus filter on K9 substrate was synthesized. The gradient-index thin film with the desired transmittance character was synthesized by Fourier-transform synthesis method, but it is difficult to fabricate. So it was divided into many homogeneous coatings with discrete refractive index. For the limited kinds of coating material, the thin film with arbitrary refractive index is not available. Based on the idea of two very thin high-low pair layers can be treated approximately as a thin layer with an average refractive index of the two layers, these coatings were replaced by homogeneous coatings. After optimization of simplex-law, the layers are composed by 183 layers of ZrO2 and SiO2. And the total thickness is 7.09 μm. The average transmittances in pass band and rejection band are 97.56% and 3.13%, respectively. And the optimizated result is better than that made with ununiform coatings and concides with the desired one. All these indicate that it is a feasible method to design coatings with any desired spectrum character, and it is possible to fabricate the coatings designed with Fourier-transform synthesis method in practice.