Recent studies report that eutectic high entropy alloys (EHEA) which possess both high strength and high ductility have potential industrial applications. In the present work, the solidification behaviors and mechanical properties of directionally solidified AlCoCrFeNi2.1 EHEA obtained at different growth velocities are investigated. The microstructure of the as-cast AlCoCrFeNi2.1 EHEA is composed of bulky dendrites (NiAl phase) and lamellar eutectic structures which consists of the CoCrFeNi (FCC) phase and the NiAl (BCC) phase. Although the actual composition of the alloy is shown to slightly deviate from the eutectic point, it is interesting to observe that the full lamellar structure of this alloy is obtained through directional solidification. In order to explain this contradiction, the maximum interface temperature criterion and the interface response function ( IRF) theory are applied to calculate the velocity range of the transition from the primary phase to the eutectic, which is 1.2 µm/s-2 × 104 μm/s. Furthermore, the tensile test indicates that the directionally solidified AlCoCrFeNi2.1 EHEA possesses a good combination of strength (1340 Mpa) and ductility (30.5%) at 100 µm/s, which can be attributed to the full lamellar eutectic structure after directional solidification. In addition, the compression tests demonstrated that the compressive strength of the axial specimen is greater than the radial specimen at the same growth velocity. Thus the directional solidification can effectively adjust the alignment of the eutectic structure and achieve better mechanical properties along the growth direction.