The semi-active inerter–based suspension system with a semi-active inerter is proposed in this article to improve the dynamic performance of the passive one. The fluid inerter is used to implement the semi-active inerter and has two adjustable inertances: the maximum and minimum inertances. Based on the relative acceleration and relative velocity between the unsprung mass and sprung mass of the suspension system, and combined with the mechanical property of the semi-active inerter, the relative-acceleration–relative-velocity control strategy is proposed and has two different types: relative-acceleration–relative-velocity ₊₋ and relative-acceleration–relative-velocity ₋₊ control strategies, respectively. The relative-acceleration–relative-velocity ₊₋ control strategy means adjusting the inertance of the semi-active inerter to the maximum one when the signs of relative acceleration and relative velocity are the same, and to the minimum one when the signs are the opposite, and the meaning of relative-acceleration–relative-velocity ₋₊ control strategy does the reverse. The dynamic response of the semi-active inerter–based suspension system with the relative-acceleration–relative-velocity control strategy is obtained using the averaging method, and its dynamic performance is evaluated using three performance indices: vehicle body acceleration, dynamic tire load, and suspension system stroke. The results show that the semi-active inerter–based suspension system with the relative-acceleration–relative-velocity ₊₋ control strategy can have a better dynamic performance for the dynamic tire load and suspension system stroke in which the low-frequency and high-frequency resonance peaks can be smaller, but is poor for the vehicle body acceleration in which the high-frequency resonance peak can be significantly larger; whereas the relative-acceleration–relative-velocity ₋₊ control strategy does the reverse. For smaller maximum and minimum inertances, the relative-acceleration–relative-velocity ₊₋ and relative-acceleration–relative-velocity ₋₊ control strategies can achieve the corresponding better performance indices, with a small degeneration for the other performance indices.