One of the disadvantages of using inorganic solid catalysts is the formation of solid waste. The use of fully-organic solid catalysts can reduce secondary pollution by simple combustion or bio-degradation. Here, an organic polymerization carrier, calix[4]resorcinarene, with polyhydroxyl characteristics, was synthesized. A cobalt containing ionic liquid was successfully chemically bonded to the hydroxyl groups on the carrier surface using 3-chloropropyltrimethoxysilane as linking agent. The resulting fully-organic supported ionic liquid catalyst was coupled with oxone for desulfurization. The micro-structure of the catalyst was composed of a porous spatial network structure. The reaction system exhibited excellent dibenzothiophene (DBT) removal (93.3%) after 90 min under the optimum experimental conditions (20 °C, 6 g of model oil with an initial sulfur content of 1000 ppm, 0.2 g of 20 wt% oxone solution with a dosage frequency of three, 15% of CoCl2, 0.15 g of catalyst, and 2 g of [Bmim]BF4). After six regeneration cycles, the sulfur removal remained above 90%. The desulfurization kinetics and mechanism were also discussed, and it was found that the hyperbolic model provided a better fit to the experimental data compared to the pseudo first-order model. The likely mechanism involves DBT being extracted using the ionic liquid [Bmim]BF4 before being oxidized by the catalyst/oxone system to form DBTO2, which is easily removed from the system using polar solvents.