To quickly start an engine and inhibit excessive load from acting on a belt connecting the engine and a starter motor when the engine is motored.

In this starting method, adjustment motoring torque, Tm* increasing with relatively large change degree is established by applying dulling process on target motoring toque, Tmtmp with using relatively small predetermined value, tc1 as a time constant tc until predetermined time, tref passes (S130, S150), and the adjustment motoring torque, Tm* increasing with relatively small change degree is established by applying dulling process on the target motoring toque, Tmtmp with using predetermined value tc2 larger than the predetermined value tc1 as the time constant tc after predetermined time tref passes (S140, S150), and the engine is motored by outputting adjustment motoring torque, Tm* from a starter motor (S160).