A transmission system of a vehicle includes a starting clutch, a change clutch, a stepped transmission, a single spindle, a gear position sensor, an actuator, and a transmission controller. The change clutch and the stepped transmission are operated via the single spindle. The gear position sensor is to detect a shift stage of the stepped transmission. The actuator is to rotate the single spindle. The transmission controller, in a case where an engine is started in a state in which the shift stage of the stepped transmission is set in second gear or higher, is configured to control the actuator to carry out shift-down operation and configured to limit output of the engine so that an engine rotation speed becomes a value smaller than a predetermined value until the shift stage of the stepped transmission is set in neutral or first gear.

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