This paper investigates a type of linear vibration isolator which incorporates two passive devices, negative stiffness elements and an inerter, into the conventional isolator (massstiffnessdamper). Two configurations of the passive devices are considered, respectively: (1) the direct parallel connection of the inerter and the negative stiffness element; (2) the series connection of the inerter with the viscous damper, which, together, is then connected with the negative stiffness element in parallel. Numerical evaluations are presented for the isolators subject to base harmonic and shock excitation, in terms of the natural frequency, the displacement transmissibility and shock isolation performance. Compared with other corresponding linear isolators, it is found that in the majority of the excitation situations, the presented isolator with the second configuration has a better performance for some isolator parameter values, that is, the inertance-to-mass ratio, the ratio of negative to positive stiffness and the damping coefficient ratio of the two dampers.