A dual-spherical friction transmission stepless speed change device comprises a box body, a speed change input shaft installed inside the box body, a speed change output shaft installed inside the box body, two friction discs, two friction transmission turning wheels installed inside the box body through swing shafts and a swing driving device used for driving the two friction transmission turning wheels to swing synchronously; the two friction discs are fixedly connected to the speed change input shaft and the speed change output shaft respectively and arranged oppositely; the two friction transmission turning wheels are located between the two friction discs and arranged symmetrically relative to the rotation axis of the friction discs; the end face, facing towards the corresponding friction transmission turning wheel, of each friction disc is provided with an arc-shaped annular groove; a spherical surface is arranged on the side face at the periphery of each friction transmission turning wheel, the sphere center of each spherical surface is overlapped with the axis of the corresponding swing shaft, and the spherical surfaces are in contact fit with the inner walls of the arc-shaped annular grooves of the two friction discs at the same time within the swing range of the friction transmission turning wheels. The dual-spherical friction transmission stepless speed change device is simple and compact in structure, long in service life, large in speed change range, good in speed change stability and easy to apply and popularize.