<p>This paper reveals a novel odd-order cascade structure for designing an odd-order bandwidth-tunable filter (BT-filter). The novel structure cascades a single first-order block and multiple second-order blocks, which removes the front-end scaling factor used in the existing cascade structure and thus simplifies the cascade configuration. To design an odd-order BT-filter using the simplified cascade structure, the most critical issue is to ensure the stability of the BT-filter. To accomplish this purpose, the paper further presents a novel converting-function alongside a coefficient-converting algorithm for ensuring the BT-filter’s stability. This tactic utilizes the new converting-function to express the BT-filter’s coefficients as the functions which definitely fulfill the stability requirement. By adopting the new odd-order cascade structure along with the stability-ensuring technique into the two-step design process, one gets a simplified odd-order BT-filter with stability ensured. The two-step process aims at minimizing the maximum deviation of the BT-filter’s amplitude response so as to generate the minimax design solution. The last part of this paper uses two tunable design examples to illustrate the ensured stability alongside the achieved high accuracy.</p>