Cobalt-free refractory high-entropy alloys (RHEAs) are strong contenders for structural materials in nuclear reactors because they do not exhibit cobalt activity under irradiation. The mechanical properties and thermal stability of RHEAs are primarily attributed to the solid solution phase, which is essentially the body-centered cubic (BCC) phase. The BCC phase formation rules thus became the basic criterion in the compositional design of RHEAs. In this paper, the BCC phase formation rules in cobalt-free RHEAs were determined via the calculation of six semiempirical parameters, namely, the entropy of mixing, enthalpy of mixing, atomic size difference, Ω-parameter, d-orbital energy level and valance electron concentration. The mixing enthalpy and atomic size differences are more effective than other semiempirical parameters for predicting BCC phase stability in cobalt-free RHEAs. The presence of aluminum is found to cause a notable alteration in the range of phase stability in cobalt-free RHEAs.