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In order to understand the quasi-static and dynamic compressive mechanical properties of carbon/epoxy composite laminates consisting of unidirectional carbon fiber plies and carbon fabric plies, several quasi-static and dynamic compression experiments were performed along three principal material axes. Dynamic compress experiments were conducted using the compression split Hopkinson’s pressure bar (SHPB) and MTS machine respectively. The experimental results showed that the materials had obvious strain rate effect. The performance of the composites in each of the three principal directions had unique characteristics. In the vertical direction of the carbon cloth, the materials had an obvious linear constitutive relationship. In-plane along the 0° carbon fiber direction, the carbon fiber controlled the mechanical properties and the strain rate effect. Specimens were also equipped with various failure modes. Failures were due to shear fractures in the normal direction and due to delamination and splitting failures in the in-plane direction. Identical tests were conducted for the unidirectional laminate. The results show that the static compressive strength and the dynamic peak stress values of fabric laminates were higher than those of unidirectional laminates under the same conditions.