This paper presents a drill-string vibration suppression method based on disturbance estimation and derivative-free model reference adaptive control (DF-MRAC) methods to address the impact of formation changing on drill-string vibration. First, a vibration suppression scheme is designed that combines disturbance estimation and DF-MRAC to counteract the effects of state-related bit-rock interaction disturbance. The bit-rock interaction disturbance containing formation information is estimated by a generalized extended state observer (GESO). Then, the drill-string vibration model without bit-rock interaction disturbance is used as the reference model. The parameters of the vibration suppression controller based on disturbance estimation and DF-MRAC are then designed, which can mitigate the effects of formation changing on vibration suppression. Finally, simulation experiments are used to illustrate the effectiveness of the proposed method in dealing with the influence of formation changing on drill-string vibration suppression. Compared to the GESO and MRAC methods, the proposed method based on DF-MRAC offers a faster and more stable vibration suppression effect.