Stacking faults, as defects of disordered crystallographic planes, are one of the most important slipping mechanisms in the commonly seen lattice, face-centered cubic (FCC). Such defects can initiate twinning which strengthens mechanical properties, e.g. twinning-induced plasticity (TWIP), of high entropy alloys (HEAs) at cryogenic temperatures. In this work, by using density functional theory (DFT), the twinning initiated from stacking faults is discussed with regard to two different solute elements, Al and Mo, in the FeNiCoCr HEAs. Our results show that adding aluminum (Al) has noticeable enhancement of twinnability while molybdenum (Mo) only induces more stacking faults in the FeNiCoCr-based HEAs.