A shift controller with a first clutch CL1 that connects/disconnects the torque to a first main shaft and a second clutch CL2 connects/disconnects the torque to a second main shaft. A transmission is configured so that dog clutches DC1, DC2 for first speed and for second speed are engaged in a predetermined turned position P1-2 of a shift drum. A linear solenoid valve that supplies clutch oil pressure, a shift solenoid that switches a destination of the supply oil pressure between both clutches and a controller that controls the supply oil pressure and the turning of the shift drum are provided. The controller supplies predetermined oil pressure P1 to the CL2 in neutral, switches the destination of supply oil pressure to the CL1 when the shift drum is turned to P1-2 according to a shift instruction to engage gears and supplies maximum oil pressure P3 to the CL1 in predetermined time ta.