Microscale SiC particles with multiwalled carbon nanotubes grow on were filled in epoxy resin to construct multiscale hybrid composite. Static and dynamic compressive responses of composites were investigated. A dynamic experimental technique, split Hopkinson press bar (SHPB), was introduced to study the constitutive laws of materials at high strain rates. SEM observations show good dispersion of carbon nanotubes and SiC particles, but bad link between SiC particles and carbon nanotubes exists. Experimental results of static and dynamic tests verify that increase of strength happens with SiC/CNT as reinforcement. Increment of strength under dynamic loading is bigger than under static loading.