Sandwich composite panels (SCPs) with carbon fibre reinforced plastic (CFRP) facings are usually vulnerable to low-velocity transverse impact loading. In this study, a method is presented to improve the impact resistance and energy absorption capacity of CFRP-faced SCPs by filling them with a concentrated styrene/acrylate particle based shear thickening fluid (STF). First, for the STF alone, aspects of mechanical performance, namely rheological and low-velocity impact behaviours, were systematically examined. It was found that the critical shear stress of the STF was lower than that of silica particle based STF with a similar particle size and volume fraction, indicating that shear thickening was more easily achieved in the styrene/acrylate particle based STF. In addition, the STF exhibited much higher energy absorption capacity than an aluminium foam. Finally, low-velocity transverse impact experiments were performed on STF-filled SCPs with two core thicknesses, 7.2 mm and 12.7 mm. It was shown that the absorbed energy of the SCPs with a thin core increased by up to 99.3%, while the impact damage of SCPs with a thick core could be effectively suppressed on the back surface of the SCPs. The impact mechanism of the STF-filled SCPs is also discussed. This study provides a new method for the design of impact-resistant SCPs.