In this study, a new type of flexible sandwich composite with nonwoven facesheets and core reinforced by polyurethane (PU) grid sealing shear thickening fluid (STF) has been presented. With the specific design, the STF was sealed into PU grids as the core to provide shear thickening effect against impact. Rheological property of STF with different mass ratio and PU morphology after first and second foaming were evaluated and optimized for sandwich composite preparation. Both static compression and dynamic impact tests were carried out to obtain the impact dynamic response and investigate the effects of typical parameters including STF volume, core thickness and striker height on low-velocity impact behavior. The test results showed that the optimal concentration of STF was 20 wt.%, whose critical shear rate was 100s−1. The presence of STF had a positive influence on the static compression strength and dynamic impact strength. In particular, the 70% STF volume fraction contributed to the highest compression modulus. The compression modulus was 445 MPa and 466 MPa when the sample thickness was 2 cm and 3 cm, respectively. As for dynamic impact strength with corresponding STF volume fractions, it was 4535.31 mJ for 30%, 4599.72 mJ for 50%, and 4827.46 mJ for 70%, all of which were much higher than that (2348 mJ) of control group (without STF). Regardless of whether the STF volume being 30%, 50% and 70%, the impact displacement of composite was within 10 mm, showing better impact resistance than control group (13.16 mm). Besides, this composite with special PU grid sealing, STF structure demonstrated a certain strain rate effect. The higher the impact energy, the greater the energy absorption was. Specifically, impact energy absorption rate of composite with a thickness of 3 cm was as high as 52.3% under 350 mm impact height.