The tension and compression of high-entropy alloy (HEA) nanowires (NWs) are remarkably asymmetric, but the micro mechanism is still unclear. In this research, the tension-compression asymmetry of AlxFeNiCrCu HEA NWs (x = 0.5, 1.0, 1.5, 2.0) was quantitatively characterized via molecular dynamics (MD) simulations, focusing on the influences of the nanowire diameter, the Al content, the crystalline orientation, and the temperature, which is exceedingly significant for applying HEAs in nanotechnology. The increased nanowire diameter improves the energy required for stacking faults nucleating, thus strengthening AlFeNiCrCu HEA NWs. A few twins during stretching weaken the strengthening effects, thereby decreasing the tension-compression asymmetry. The increased Al content raises the tension-compression asymmetry by promoting the FCC to BCC phase transition during stretching. The tension along the [001] crystalline orientation is stronger than the compression, while [110] and [111] crystalline orientations are entirely opposite, and the tension-compression asymmetry along the [111] crystalline orientation is the minimum. The diversities in the tension-compression asymmetry depends on the deformation mechanism. Compressing along the [001] crystalline orientation and stretching along the [110] crystalline orientation induces twinning. Deformation along the [111] crystalline orientation only leaves stacking faults in the nanowires. Therefore, the tension and compression along the [111] crystalline orientation exhibit minimal asymmetry. As the temperature rises, the tension-compression asymmetry along [001] and [111] crystalline orientations increases, while that along the [110] crystalline orientation decreases.