A running control device of a vehicle including an engine , wheels , a connecting/disconnecting device (C1) disposed between the engine and the wheels , the connecting/disconnecting device (C1) being placed in an engaged state for connecting the engine and the wheels and placed in a released state for disconnecting the engine and the wheels , the running control device further including a brake operation member operated depending on a brake request amount (Brk) of a driver, and a brake booster amplifying a brake force by using a negative pressure generated by rotation of the engine, the running control device of a vehicle being configured to execute an engine brake running mode performed with the engine coupled to wheels such that an engine brake is applied by driven rotation of the engine and an inertia running mode performed with an engine brake force made lower than that in the engine brake running mode, the running control device of a vehicle executing a first inertia running mode performed with the connecting/disconnecting device (C1) placed in the released state with the rotation of the engine stopped and a second inertia running mode performed with the connecting/disconnecting device (C1) placed in the released state with the engine kept rotating in accordance with predefined respective execution conditions as the inertia running mode, the running control device of a vehicle being characterized in that the brake request amount (Brk) is included as a condition for terminating the inertia running mode, the first inertia running mode is terminated when the brake request amount becomes equal to or greater than a predefined first determination value (α) while the first inertia running mode is performed, and the second inertia running mode is terminated when the brake request amount becomes equal to or greater than a predefined second determination value (β) larger than the first determination value while the second inertia running mode is performed. the running control device of a vehicle being configured to execute an engine brake running mode performed with the engine coupled to wheels such that an engine brake is applied by driven rotation of the engine and an inertia running mode performed with an engine brake force made lower than that in the engine brake running mode, the running control device of a vehicle executing a first inertia running mode performed with the connecting/disconnecting device (C1) placed in the released state with the rotation of the engine stopped and a second inertia running mode performed with the connecting/disconnecting device (C1) placed in the released state with the engine kept rotating in accordance with predefined respective execution conditions as the inertia running mode, the running control device of a vehicle being characterized in that the brake request amount (Brk) is included as a condition for terminating the inertia running mode, the first inertia running mode is terminated when the brake request amount becomes equal to or greater than a predefined first determination value (α) while the first inertia running mode is performed, and the second inertia running mode is terminated when the brake request amount becomes equal to or greater than a predefined second determination value (β) larger than the first determination value while the second inertia running mode is performed. <EOS>