A pedal driving mechanism for a bicycle which contains structurally improved pedal arms on which pedals are installed to increase the rotary radius of the pedals during the running of the bicycle to obtain optimum driving energy with minimum physical energy consumption, wherein the structure of pedaling mechanism defines a joining line formed by the tooth-coupling of a fixing gear and a rotary gear with the axle line of a driving arm at a right angle, and the trace of the linkage formed by a connection arm and a connection link is set to move in a spiral motion forced to rotate with respect to the center of the fixing gear.