To provide a waste oil combustion device for efficiently burning waste oil having a high fire point to be rendered harmless while suppressing the incomplete combustion.

A wick case 51 is arranged on a bottom face 10b of a combustion furnace 10. In the wick case 51, a wick 52 is placed which is formed of glass fibers or porous ceramics. The waste oil supplied from a waste oil supply device 20 is dropped onto the wick case 51 to permeate into the wick 52. A blower 30 blows air to the wick 52 into which the waste oil permeates for complete combustion.