The deformation behavior of single-crystal materials is closely related to the crystallographic orientation. However, there are few simulations and experimental studies on the effect of crystallographic orientation on the tensile properties of single-crystal AlxCoCrFeNi high entropy alloys (HEAs). Molecular dynamics simulations were used to analyze the mechanical properties and structural variations of Al0.25CoCrFeNi HEAs with different crystallographic orientations under tension. Prior to yielding, elastic softening occurred in [111], [110] and [11̅0]-oriented HEAs, except for [100]-oriented HEA. During plastic deformation, [100]-oriented HEA had high strength and flow stress due to the low Schmid factors of leading partial dislocations and multiple activatable slip systems. [111]-oriented HEA also showed high strength and flow stress, which were attributed to the low Schmid factors of the activatable slip systems and the existence of incomplete stacking fault tetrahedrons. Both [110]- and [11̅0]-oriented HEAs showed low strength, but the presence of the secondary increased stress suggested they had good plasticity. The difference between them was that [110]-oriented HEA was easier to form hexagonal close-packed lamellae and experienced secondary yielding at larger strain. This suggested that different crystallographic orientations in the non-tensile direction also affected the mechanical properties.