This paper first presents a novel function for simplifying the stability guarantee of a tunable bandpass filter with a tunable center-frequency (TCF), and then develops a complexity-reduction strategy for attaining a complexity-reduced TCF bandpass filter. Based on the two novel schemes, an L1-norm approximation formulation is developed for producing a TCF bandpass filter with significantly reduced complexity as well as simplified stability guarantee. The resulting L1-error-minimized TCF bandpass filter demonstrates that the complexity can be reduced by nearly \(35\%\) , while the approximation accuracy remains approximately the same. Furthermore, the presented new function along with the simplified parameter-converting strategy simplifies the stability-guarantee process, which does not require a constant factor to scale the parameter conversions. As a result, the designed TCF bandpass filter has a greatly reduced complexity and it also remains stable.