Inspired that kangaroo can buffer the impact and absorb vibration from the ground and keep the whole-body stable, an integrated kangaroo bio-inspired vibration suppression (IKBVS) structure considering vibration isolation-absorption simultaneously is proposed for low/wide band frequency vibration control. Based on skeleton mass, articulation friction, and the synergistic action among skeleton, articulation, and muscle/tendon, a vibration suppression model with more biological basic characteristics is derived. The validity of model and method is confirmed, and the static and dynamic analysis of the IKBVS system is carried out to investigate the vibration suppression performance. The quasi-zero stiffness region can be achieved with a smaller initial installation angle, medium rod length, smaller foot stiffness, and slightly lighter isolated mass in a wide displacement interval. The coupling mechanism of vibration isolation-absorption is revealed by parameter analysis. The results indicate that the IKBVS structure has favorite dynamic properties due to adjustable nonlinearity, namely, lower and adjustable resonance and anti-resonance frequency/peak and different levels of vibration suppression effect in high-frequency range are achieved readily. This research provides new insight into application of bio-inspired vibration suppression structures in various engineering systems for better vibration control.