In this work,we report implementation of the equation of motion coupled-cluster method for double ionized states(EOMDIP-CC)with spin-orbit coupling(SOC)using closed-shell state as reference.Ionized 2h and 3h1p space are taken into consideration in calculation of double ionization potentials(DIPs)with EOM at the CC singles and doubles levels(CCSD).Time-reversal symmetry together with spatial symmetry is exploited by to reduce computational effort.Some charge-stabilization methods are applied in EOMDIP-CC calculations to stabilize unstable reference function and extrapolation is employed to reach the final results.Ground and some low-lying states of Xe2+,Cd2+,I+,Ag+ and Te as well as SeO and TeO with two unpaired electrons have been calculated by EOMDIP-CCSD.These systems with two additional electrons are used as references.For atoms or molecules with a stable reference,splitting of the states due to SOC based on EOMDIP-CCSD agrees well with experimental data.On the other hand,results are poor for systems with unstable reference,i.e.reference with two negative charges.Extrapolation combined with charge-stabilization methods is employed to improve results.These results show that this approach is able to afford reasonable estimates for SOC splitting.