In spite of worldwide research, carbon nanotubes (CNTs) still have not fully realized their original promise as ideal reinforcements for composite materials due to a number of challenging issues such as weak interface, poor dispersion, misalignment and lack of optimized design. Here we propose a bio-inspired structure of CNT bundles with controllable crosslink density and staggered pattern of organization that mimic the architecture of natural collagen fiber. Molecular mechanics (MM) simulations show that, under tensile loading, the bio-inspired CNT bundles undergo a transition in failure mode from CNT pull-out to CNT break as the crosslink density increases, with strength an order of magnitude higher than that of the existing strongest conventional carbon fibers. Based on the MM simulations, a generalized tension-shear chain model with four dimensionless parameters is developed to guide the design of CNT bundles for optimized mechanical properties.