A liquid crystal (LC)-modulated tunable filter is theoretically studied, consisting of an Au nanorod array and an Au film separated by a dielectric indium tin oxide (ITO) glass layer. It is well established that this system can achieve double absorptive peaks resulting from the strong plasmonic coupling between the plasmon-induced transparency effect of the nanorod array and the cavity mode of the Au microcavity structure. The positions of the double absorptive peaks can be tuned dynamically based on the electro-optic effect of LC. The simulation results reveal that a band range of 160 nm has been confirmed at near-infrared wavelengths by altering the driven voltage of LC from 0 to 8 V. The proposed structure is able to filter the two peaks with the reflection coefficients <5 % . Compared with the existing tunable filter, it has many advantages, such as continuous tunability, low tuning voltage, and great degree of tunability.