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In the paper an application of a particle swarm optimization to the design of stable IIR digital filters with non-standard amplitude characteristics is presented. Particle swarm algorithms are newly elaborated technique for optimization of multi-modal functions, as for example functions describing the problem of calculation of an optimal set of transfer function coefficients in which the gradient algorithms can easily stick at local extreme. Design of IIR digital filters with non-standard amplitude characteristics which considerably differ from typical Butterworth, Chebyshev, and Cauer approximations, is possible using presented method. The IIR digital filter with linearly falling amplitude characteristics is designed with the use of proposed method. The filter is stable and fulfill all prescribed design assumptions.