The invention provides a conical surface friction transmission reduction gearbox. The invention comprises a reduction gearbox casing body and a planetary wheel system, a central wheel is fixedly connected on an input axle, a planetary wheel bearing seat is hinged with a planetary frame, the planetary frame is fixedly connected on the output axle. The planetary wheel, the central wheel and the fixed wheel are all conical surface wheels, the included angle Theta of the planetary wheel axial line and the central wheel axial line is larger than zero, and an elastic device is arranged at one hinging end of each planetary wheel bearing seat and the planetary frame. The reduction gearbox adopts a conical surface friction transmission planetary wheel system structure, only a very small axial pushing force is provided to the planetary wheel axial direction, to generate the radial positive pressure of a plurality of times of the axial pushing force, and the axial pressure can provide the pressure required by the friction transmission. Relevant to the prior reduction gearbox, the invention has the advantages that the structure is simple, the weight is light, the volume is small, the transmission efficiency is high, the service life is long, the overload protection can be performed, lubricating oil is not required to perform lubrication, the deceleration ratio is high, the running is smooth, the manufacture process is simple, and the using and maintenance cost is low.