Strong and uniform carbon nanotube (CNT) fibers with tensile strength around 1.2 GPa were prepared from vertically aligned CNT arrays, and their mechanical properties were studied using a wide range of tensile strain rates. The cyclic load/unload process, polarized Raman measurements, and fiber fracture surfaces were also used to study the failure mechanism of the CNT fibers. It is found that the fibers exhibit a strain-rate strengthening effect, and have different failure mechanisms at high and low strain rates. The key factors that limit the mechanical properties of the CNT fibers were then investigated based on a failure mechanism analysis: inter-tube slippage happens at low strain-rates, and “cascade-like” breaking dominates at high strain-rates. The maximum strength of the fibers appears at high strain rates, and is mainly determined by the CNT alignment.