A type of quasi-isotropic carbon/epoxy composites was prepared. In order to study the dynamic mechanical properties of composites, the compressive specimens were investigated in the normal direction, as well as in the in-plane direction at different strain rates by Hopkinson pressure bar (SHPB) technique. The macro- and micro-fracture morphology of the damaged specimens was obtained utilizing the scanning electron microscope (SEM). The experimental results showed that the dynamic stress-strain behaviour can be significantly affected by the strain rates. As the strain rates increased, the maximum strength and maximum modulus increased, the ultimate strain reduced. The compressive strength and the ultimate strain in the in-plane direction are obviously lower than that in the normal direction. The main way of the dynamic compressive failures in the normal direction is shear failure due to the brittle fracture of the fibre. Interfacial crack and delamination can be produced in the in-plane direction.