Design methods for digital filters with sparse coefficients (0 coefficients) are beneficial for reduction of arithmetic cost. Although the number of multipliers of the filter (arithmetic cost) can be reduced by using 0 coefficients, the performance of the filter can be degraded. In this paper, we propose a design method for multi-band digital filters with not only the sparse coefficients but also the sameness conditions of filter coefficients in which the absolute values of some coefficients are same. It is expected that the performance of the filter with the sameness conditions of filter coefficients can be better than that with just the sparse coefficients. Since the design problem is to optimize the combination of the sameness conditions and compute the real values of filter coefficients, the design problem is more complicated than that of the sparse filters. In order to optimize the combination of the sameness conditions, we employ a genetic algorithm (GA). Also, the real coefficients can be computed based on the Lagrange multiplier method. Finally, we show a design example in order to demonstrate the effectiveness of the proposed method.