The tensile properties of carbon nanotube (CNT) fibers have been widely studied. However, the knowledge of their compressive properties is still lacking. In this work, the compressive properties of both pure CNT fibers and epoxy infiltrated CNT fibers were studied using the tensile recoil measurement. The compressive strengths were obtained as 416 and 573 MPa for pure CNT fibers and CNT–epoxy composite fibers, respectively. In addition, microscopic analysis of the fiber surface morphologies revealed that the principal recoil compressive failure mode of pure CNT fiber was kinking, while the CNT–epoxy composite fibers exhibited a failure mode in bending with combined tensile and compressive failure morphologies. The effect of resin infiltration on CNT fiber compressive properties, including the compressive strength and the deformation mode, is discussed. This work expands the knowledge base of the overall mechanical properties of CNT fibers, which are essential for their application in multifunctional composites.