Acetic anhydride is a typical precursor chemical. There is little research on semiconductor sensors to acetic anhydride at present, and the operating temperatures of these sensors are relatively high. Therefore, it is important to be able to prepare sensors with good gas-sensing performance to acetic anhydride at lower temperatures. Considering that spinel semiconductor sensors have advantages in operating temperature, and p-type semiconductor sensors are more suitable for preparing low-temperature sensors than n-type semiconductors, ZnCo2O4 was used to detect acetic anhydride in this study. Bare ZnCo2O4 was prepared by coprecipitation method and then modified with In2O3 by hydrothermal method. The sensor was tested to have the best gas-sensing performance to acetic anhydride at $180~^{\circ }$ C, which was well below the operating temperature of current acetic anhydride gas sensors. Besides, the sensor had a low detection limit (0.5 ppm) for acetic anhydride, and had good selectivity and stability. Finally, the mechanism of the enhanced performance of the sensor modified by In2O3 was analyzed from the viewpoints of synergistic catalysis and p-n heterojunction.