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In this paper, a novel genetic algorithm, which is called a hybrid Taguchi-genetic algorithm (HTGA), is proposed to solve the design problem of two-dimensional (2D) recursive digital filters. The HTGA approach is a method of combining the traditional genetic algorithm (TGA), which has a powerful global exploration capability, with the Taguchi method, which can exploit the optimum offspring. The Taguchi method is inserted between crossover and mutation operations of the TGA. Then, the systematic reasoning ability of the Taguchi method is incorporated in the crossover operations to select the better genes to achieve crossover, and consequently enhance the genetic algorithms. Therefore, the HTGA approach can be more robust statistically sound, and quickly convergent. The proposed HTGA approach is effectively applied to test on a 2D filter example and is compared with previous design methods. The design of the 2D filter is reduced to a constrained minimization problem the solution of which is achieved by the convergence of the HTGA. The computational experiments show that the HTGA approach can obtain better results than previous design methods.