A control apparatus in combination with an engine, the control apparatus is to be provided in a vehicle, the vehicle including (i) the engine that is used as a drive force source for driving the vehicle, and (ii) an automatic transmission that constitutes a part of a drive-force transmitting path between the engine and drive wheels of the vehicle, wherein the control apparatus comprises an engine-brake control portion configured to calculate a target speed value (Net) of a rotational speed (Ne) of the engine that is required to provide a required torque value (Tebd) of an engine brake torque (Teb), wherein the engine-brake control portion is configured to control shifting of the automatic transmission such that the rotational speed (Ne) of the engine is approximated to the target speed value (Net) of the rotational speed (Ne) of the engine, wherein the engine-brake control portion is configured to determine whether the target speed value (Net) of the rotational speed (Ne) of the engine exceeds a predetermined threshold value (α), and wherein, when the target speed value (Net) exceeds the predetermined threshold value (α), the engine-brake control portion is configured to control the shifting of the automatic transmission such that the rotational speed (Ne) of the engine is held not higher than the predetermined threshold value (α), characterized in that: the engine is configured with an engine brake characteristic that the engine brake torque (Teb) is higher when the throttle valve is controlled to be opened than when the throttle valve is fully closed as long as the rotational speed (Ne) of the engine is not lower than a certain speed value, the predetermined threshold value (α) of the rotational speed (Ne) of the engine is higher than the certain speed value (Nel) of the rotational speed (Ne) of the engine; and when the target speed value (Net) exceeds the predetermined threshold value (α), the engine brake control portion is configured additionally to control a throttle valve of the engine such that the throttle valve is opened. wherein the control apparatus comprises an engine-brake control portion configured to calculate a target speed value (Net) of a rotational speed (Ne) of the engine that is required to provide a required torque value (Tebd) of an engine brake torque (Teb), wherein the engine-brake control portion is configured to control shifting of the automatic transmission such that the rotational speed (Ne) of the engine is approximated to the target speed value (Net) of the rotational speed (Ne) of the engine, wherein the engine-brake control portion is configured to determine whether the target speed value (Net) of the rotational speed (Ne) of the engine exceeds a predetermined threshold value (α), and wherein, when the target speed value (Net) exceeds the predetermined threshold value (α), the engine-brake control portion is configured to control the shifting of the automatic transmission such that the rotational speed (Ne) of the engine is held not higher than the predetermined threshold value (α), characterized in that: the engine is configured with an engine brake characteristic that the engine brake torque (Teb) is higher when the throttle valve is controlled to be opened than when the throttle valve is fully closed as long as the rotational speed (Ne) of the engine is not lower than a certain speed value, the predetermined threshold value (α) of the rotational speed (Ne) of the engine is higher than the certain speed value (Nel) of the rotational speed (Ne) of the engine; and when the target speed value (Net) exceeds the predetermined threshold value (α), the engine brake control portion is configured additionally to control a throttle valve of the engine such that the throttle valve is opened. the engine is configured with an engine brake characteristic that the engine brake torque (Teb) is higher when the throttle valve is controlled to be opened than when the throttle valve is fully closed as long as the rotational speed (Ne) of the engine is not lower than a certain speed value, the predetermined threshold value (α) of the rotational speed (Ne) of the engine is higher than the certain speed value (Nel) of the rotational speed (Ne) of the engine; and when the target speed value (Net) exceeds the predetermined threshold value (α), the engine brake control portion is configured additionally to control a throttle valve of the engine such that the throttle valve is opened.