A comprehensive investigation of the mechanical behavior and microstructural evolution of carbon nanotube (CNT) continuous fibers under twisting and tension is conducted using coarse-grained molecular dynamics simulations. The tensile strength of CNT fibers with random CNT stacking is found to be higher than that of fibers with regular CNT stacking. The factor dominating the mechanical response of CNT fibers is identified as individual CNT stretching. A simplified twisted CNT fiber model is studied to illustrate the structural evolution mechanisms of CNT fibers under tension. Moreover, it is demonstrated that CNT fibers can be reinforced by enhancing intertube interactions. This study would be helpful not only in the general understanding of the nano- and micro-scale factors affecting CNT fibers' mechanical behavior, but also in the optimal design of CNT fibers' architecture and performance.