This paper proposes a novel inerter-based dynamic vibration absorber, namely, electromagnetic resonant shunt tuned mass-damper-inerter (ERS-TMDI). To obtain the performances of the ERS-TMDI, the combined ERS-TMDI and a single degree of freedom system are introduced. criteria performances of the ERS-TMDI are introduced in comparison with the classical tuned mass-damper (TMD), the electromagnetic resonant shunt series TMDs (ERS-TMDs), and series-type double-mass TMDs with the aim to minimize structure damage and simultaneously harvest energy under random wind excitation. The closed form solutions, including the mechanical tuning ratio, the electrical damping ratio, the electrical tuning ratio, and the electromagnetic mechanical coupling coefficient, are obtained. It is shown that the ERS-TMDI is superior to the classical TMD, ERS-TMDs, and series-type double-mass TMDs systems for protection from structure damage. Meanwhile, in the time domain, a case study of Taipei 101 tower is presented to demonstrate the dual functions of vibration suppression and energy harvesting based on the simulation fluctuating wind series, which is generated by the inverse fast Fourier transform method. The effectiveness and robustness of ERS-TMDI in the frequency and time domain are illustrated.