The tension and compression of face-centered-cubic high-entropy alloy (HEA) nanowires are significantly asymmetric, but the tension-compression asymmetry in nanoscale body-centered-cubic (BCC) HEAs is still unclear. In this study, the tension-compression asymmetry of the BCC AlCrFeCoNi HEA nanowire is investigated using molecular dynamics simulations. The results show a significant asymmetry in both the yield and flow stresses, with BCC HEA nanowire stronger under compression than under tension. The strength asymmetry originates from the completely different deformation mechanisms in tension and compression. In compression, atomic amorphization dominates plastic deformation and contributes to the strengthening, while in tension, deformation twinning prevails and weakens the HEA nanowire. The tension-compression asymmetry exhibits a clear trend of increasing with the increasing nanowire cross-sectional edge length and decreasing temperature. In particular, the compressive strengths along the [001] and [111] crystallographic orientations are stronger than the tensile counterparts, while the [110] crystallographic orientation shows the exactly opposite trend. The dependences of tension-compression asymmetry on the cross-sectional edge length, crystallographic orientation, and temperature are explained in terms of the deformation behavior of HEA nanowire as well as its variations caused by the change in these influential factors. These findings may deepen our understanding of the tension-compression asymmetry of the BCC HEA nanowires.