A novel approach is established for fabricating high-strength and high-stiffness composite laminates with continuous carbon nanotube (CNT) yarns for scaled-up mechanical tests and potential engineering applications. Continuous CNT yarns with up to 80% degree of nanotube alignment and a unique self-assembled graphitic CNT packing result in their specific tensile strengths up to 1.9 N/tex. Unidirectional CNT yarn reinforced composite laminates with a CNT concentration of greater than 80 wt.% and minimal microscale voids are fabricated using filament winding and aerospace-grade resin matrices. A specific tensile strength of up to 1.71 GPa/(g cm-3) and a specific modulus of 256 GPa/(g cm-3) are realized; the specific modulus exceeds current state-of-the-art IM7, T1100G and even M60J unidirectional carbon fiber composite laminates. The results demonstrate an effective approach transferring high-strength CNT yarns into composites for applications that require specific tensile modulus properties that are significantly beyond state-of-the-art carbon fiber composites, and potentially open a new performance region in the Ashby chart for composite material applications.