A shift drive mechanism in which a special constant-meshing-type multi-speed transmission can be applied to a transmission case of a constant-meshing-type multi-speed transmission of a general type. In a shift drive mechanism of a multi-speed transmission where the transmission is configured such that a control rod is movable in the axial direction on a hollow-shaft center axis of a gear shaft formed in a hollow shape so that an engagement changeover mechanism is driven to perform a gear shift, and a shift pin, which is guided by a shift drum provided near a periphery of the gear shaft, moves the control rod in the axial direction, an intermittent drive mechanism intermittently rotates the shift drum for every position of each gear speed by transmitting the reciprocating rotation of a shift spindle, which is connected to a gear shift operating member, is arranged between the shift spindle and the shift drum.