Rare-earth-substituted REBa2Cu4O8 phases (RE124) are synthesized by using molten KOH to investigate phase formation and superconductivity. RE124 phases with small and heavy rare-earth elements of Yb, Er, Ho, Dy, Gd and Y are easily producible with good superconducting properties and crystallinity. Superconducting transition temperature and superconducting volume fraction decrease with increasing ion radius of the rare-earth elements. Samples using large rare-earth elements show broad peaks of RE124 pattern in x-ray diffraction also with broad peaks probably originating from RE123 and other related phases.