This paper proposes the use of a novel type of passive vibration control system to reduce vibrations in civil engineering structures subject to base excitation. The new system is based on the inerter, a device that was initially developed for high-performance suspensions in Formula 1 racing cars. The principal advantage of the inerter is that a high level of vibration isolation can be achieved with low amounts of added mass. This feature makes it an attractive potential alternative to traditional tuned mass dampers (TMDs). In this paper, the inerter system is modelled inside a multi-storey building and is located on braces between adjacent storeys. Numerical results show that an excellent level of vibration reduction is achieved, potentially offering improvement over TMDs. The inerter-based system is compared to a TMD system by using a range of base excitation inputs, including an earthquake signal, to demonstrate how the performance could potentially be improved by using an inerter instead of a TMD. Copyright © 2013 John Wiley & Sons, Ltd.