Co-Fe-Mg-Al quaternary hydrotalcite-carbon nanotube composites (LDH-CNT composites) were prepared by co-precipitation method and blended into concrete. Universal testing machine and SHPB testing device were used to carry out static and dynamic tests on LDH-CNT concrete specimens with different LDH-CNT additions (0, 0.25 wt.%, 0.5 wt.%), and the dynamic constitutive equation was obtained according to the dynamic stress-strain curve. Results show that compared with ordinary concrete, the compressive strength and toughness of LDH-CNT concrete have been greatly improved. When the LDH-CNT composites content is 0.5 wt.%, the strength and toughness are increased by 10.8% and 16.3%, respectively; The dynamic compression mechanical properties of LDH-CNT concrete show a significant strain rate effect, and the impact compression mechanical parameters increase with the increase of the maximum strain rate. In the strain rate range of 10°∼102s−1, the theoretical curve and the measured curve fit better, and the constitutive equation can describe the dynamic mechanical response of LDH-CNT concrete.