To reduce the load alternately imposed on the rider's legs when the pedals are stepped and to use the muscle of the entire legs in a well balanced manner, thereby naturally returning the pedals to the initial position of the stepping operation without forming an unnatural bending state of each leg at the returning track of the pedal. A crank mechanism for a bicycle comprises a main crank (9), a follower crank (12), and a connecting lever (15) disposed between free ends of the cranks (9, 12), a second fixed fulcrum shaft (11) of the follower crank (12) being arranged at a location obliquely upward and backward of a first fixed fulcrum shaft (8) of the main crank (9), the follower crank (12) being extended downward beyond a line (L2) connecting the first and second fixed fulcrum shafts (8), (11) from the second fixed fulcrum shaft (11) such that a second free fulcrum shaft (11) at its free end is swung below the line (L2) connecting the first and second fixed fulcrum shafts (8, 11), a pedal (16) being attached to a projection end (17) in the vicinity of a first free fulcrum shaft (13) of the lever (15) and arranged in the vicinity of the free end of the main crank (9), the pedal (16) being rotated along a non-circular track (T) passing through the first and second fixed fulcrum shafts (8 and 11), and the first fixed fulcrum shaft (8) being located at an internal area of the track (T).