Solid-state potassium batteries are promising energy storage systems, but their wide use requires suitable solid electrolytes to ensure high ionic conductivity, electrochemical stability, and contacting ability with composite electrodes. For this purpose, this study introduces sulfone-based crystalline organic electrolytes (SCOEs) consisting of dimethyl sulfone (DMS) and potassium bis(fluorosulfonyl)imide (KFSI). One solid-state SCOE, KFSI/DMS 1:9 by mol, exhibits high ionic conductivity (4.0 × 10⁻⁴ S cm⁻¹ at 25 °C), oxidation stability (~5.8 V vs. K⁺/K), and negligible flammability. Moreover, owing to its optimal melting point (94 °C), the SCOE enables seamless contact with the composite electrodes through the melt-casting process, which has been challenging for other solid-state electrolytes. K||KVPO₄F cells filled with this SCOE show improved cycle performance (capacity retention 88.8% after 100 cycles vs. 77.6% after 74 cycles at 25 °C) with high Coulombic efficiency (asymptotic value 99.6% vs. 92.0%) compared to cells with a conventional carbonate electrolyte. With these results, the developed SCOE paves the way to room-temperature operable, 5 V solid-state potassium batteries.