When a transducer is put on an aural cartilage, the transmitted vibration generates sound in the external auditory canal (i.e., cartilage conduction). Different from conventional earphones, the cartilage conduction technology enables the use of earphones without occluding the canal. However, the opening ears allow both desired sounds (e.g., speech) and unwanted noises to reach the eardrums. To minimize only the noise selectively, our study introduced filtered-x least means square algorithm combined with adaptive bandpass filter (ABF-FxLMS). The ABF-FxLMS stored the narrowband noise separating from a speech and transferred it to the FxLMX as a secondary sound source produced via the cartilage conduction. The adaptive bandpass filter actively adjusted to changes in the center frequency of noise, and the ABF-FxLMS ensured effective noise reduction permitting the passing of speech. Our simulations demonstrated achieving approximately 19 dB reduction in the noise while keeping the speech quality. A coming cartilage conduction device will enable conversations in noisy environments.