In this work, we assume that the observed state Ξ(1620) is a s-wave ΛK or ΣK bound state. Based on this molecule picture, we establish the Bethe-Salpeter equations for Ξ(1620) in the ladder and instantaneous approximations. We solve the Bethe-Salpeter equations for the ΛK and ΣK systems numerically and find that the Ξ (1620) can be explained as ΛK and ΣK bound states with J P = 1/2 − , respectively. Then we calculate the decay widths of Ξ(1620) → Ξπ in these two different molecule pictures systems, respectively.