High-entropy alloys (HEAs) break the design concept of traditional alloys and exhibit excellent mechanical properties. However, as a new member of the alloy family in recent years, the dependence of the deformation behavior of the HEAs on alloy composition and twin boundary (TB) is still unclear, and many phenomena urgently need to be revealed. Here, the effects of TB spacing and Ni concentration on the mechanical properties and deformation behavior of the nano-twinned (CoCrFeCu)1−XNiX HEA (nt-HEA) under tensile loading are investigated by molecular dynamics simulation. The results show that with the decrease in TB spacing, the average flow stress of the nt-HEA changes from Hall–Petch strengthening to inverse Hall–Petch softening. When the TB spacing is greater than a critical value, the plastic deformation mechanism is dominated by the slip of partial dislocations. However, when the TB spacing is less than the critical value, the plastic deformation mechanism is transformed into the formation of voids induced by the amorphous phase, which becomes the key factor for the softening of the nt-HEA. It is also found that the mechanical properties of the nt-HEA can also change from strengthening to softening by adjusting Ni concentration, which is closely related to the change of stacking fault energy of the nt-HEA. In addition, the plastic deformation mechanism and voids formation mechanism of the nt-HEA are also discussed in detail.