The invention discloses a friction wheel transmission stepless transmission bicycle, which comprises a bicycle frame, handlebars, a speed regulating handle, a front wheel, pedals, a front flywheel, a chain, a back flywheel, a rotating direction changing device, a rotating shaft, a friction wheel transmission device, a speed regulating device, a back wheel and a back wheel axle, wherein the rotating direction changing device comprises two mutually engaged bevel gears, one bevel gear is synchronously connected with the back fly wheel, the other bevel gear is connected with the rotating shaft, further, the rotating input of the rotating shaft is realized, the friction wheel transmission device comprises a friction disc, a spring, a regulating screw nut and a friction wheel, the friction disc, the spring and the regulating screw nut are arranged on a back axle, the friction wheel synchronously rotates with the rotating shaft, one end of the rotating shaft is provided with a spline, a friction wheel is glidingly connected onto the spline position, and the friction wheel is in vertical and tight contact with the friction disc. The friction wheel transmission stepless transmission bicycle has the advantages that the stable speed change can be realized under any road conditions, the speed change amplitude is great, the speed change is stable, meanwhile, through the modification on the existing bicycle, the manufacturing is simple, the cost is low, economic performance and reasonableness are realized, and the applicability is high.