A control apparatus for a hybrid vehicle that comprises: an internal combustion engine comprising a valve stop mechanism (36, 38) capable of stopping at least one valve among an intake valve and an exhaust valve in a closed state, and a catalyst (24, 26) that purifies exhaust gas; a motor that is an electric motor that, together with the internal combustion engine, constitutes a power source of the vehicle, and that is capable of driving an output shaft of the internal combustion engine that is in a stopped state; poisoning state estimation means that estimates a rich poisoning state of the catalyst (24, 26) based on an operating state of the internal combustion engine; fuel-cut operation control means that, when a predetermined fuel-cut operation condition is established during operation of the internal combustion engine, executes a fuel-cut operation that stops a fuel supply to the internal combustion engine; valve operation control means that, during the fuel-cut operation, controls the valve stop mechanism (36, 38) and executes valve stopping in case where it is estimated by the poisoning state estimation means that the catalyst (24, 26) is not in a rich poisoning state, or a temperature of the catalyst (24, 26) is higher than a predetermined determination temperature, and the valve operation control means that, during the fuel-cut operation, prohibits valve stopping in case where it is estimated that the catalyst (24, 26) is in a rich poisoning state, and a temperature of the catalyst (24, 26) is less than or equal to the determination temperature; and engine idling means that, during the fuel-cut operation, when valve stopping with respect to the valve (32, 34) is prohibited by the valve operation control means, drives the output shaft of the internal combustion engine by means of the motor and supplies oxygen to the catalyst (24, 26). an internal combustion engine comprising a valve stop mechanism (36, 38) capable of stopping at least one valve among an intake valve and an exhaust valve in a closed state, and a catalyst (24, 26) that purifies exhaust gas; a motor that is an electric motor that, together with the internal combustion engine, constitutes a power source of the vehicle, and that is capable of driving an output shaft of the internal combustion engine that is in a stopped state; poisoning state estimation means that estimates a rich poisoning state of the catalyst (24, 26) based on an operating state of the internal combustion engine; fuel-cut operation control means that, when a predetermined fuel-cut operation condition is established during operation of the internal combustion engine, executes a fuel-cut operation that stops a fuel supply to the internal combustion engine; valve operation control means that, during the fuel-cut operation, controls the valve stop mechanism (36, 38) and executes valve stopping in case where it is estimated by the poisoning state estimation means that the catalyst (24, 26) is not in a rich poisoning state, or a temperature of the catalyst (24, 26) is higher than a predetermined determination temperature, and the valve operation control means that, during the fuel-cut operation, prohibits valve stopping in case where it is estimated that the catalyst (24, 26) is in a rich poisoning state, and a temperature of the catalyst (24, 26) is less than or equal to the determination temperature; and engine idling means that, during the fuel-cut operation, when valve stopping with respect to the valve (32, 34) is prohibited by the valve operation control means, drives the output shaft of the internal combustion engine by means of the motor and supplies oxygen to the catalyst (24, 26).