The tensile properties of continuous carbon nanotube (CNT) fibers spun from a CNT carpet consisting of mainly double- and triple-walled tubes, and their interfacial properties in an epoxy matrix, are investigated by single fiber tensile tests and microdroplet tests, respectively. The average CNT fiber strength, modulus and strain to failure are 1.2 ± 0.3 GPa, 43.3 ± 7.4 GPa and 2.7 ± 0.5%, respectively. A detailed study of strength distribution of CNT fiber has been carried out. Statistical analysis shows that the CNT fiber strength is less scattered than those of MWCNTs as well as commercial carbon and glass fibers without surface treatment. The effective CNT fiber/epoxy interfacial shear strength is 14.4 MPa. Unlike traditional fiber-reinforced composites, the interfacial shear sliding occurs along the interface between regions with and without resin infiltration in the CNT fiber. Guidelines for microdroplet experiments are established through probability analysis of variables basic to specimen design.