An apparatus for controlling an engine air intake system having: an intake passage having a first air intake passage portion and a second air intake passage portion for supplying air to the engine; first and second variable intake control valves (11, 12) arranged between the first and second intake passage portions (2a, 2b) for selectively opening and closing communication between the first and second intake passage portions (2a, 2b); a vacuum tank for storing negative pressure; first and second actuators (43, 44) for independently driving each of the first and second variable intake control valves (11, 12) between an open state and a closed state using the negative pressure in the vacuum tank; and a one-way valve arranged between the vacuum tank and the intake passage for selectively permitting communication between the vacuum tank and the intake passage; the apparatus, being characterised by comprising: control means arranged to control the first and second actuators (43, 44) to offset operating timings of the first and second variable intake control valves (11, 12) when the first and second variable intake control valves (11, 12) are switched according to an increase of the engine rotational speed from a first operating state in which the first and second variable intake control valves (11, 12) are both in the open state by default due to a spring force to a second operating state in which the first and second variable intake control valves (11, 12) are both in the closed state adjusted by the negative pressure. an intake passage having a first air intake passage portion and a second air intake passage portion for supplying air to the engine; first and second variable intake control valves (11, 12) arranged between the first and second intake passage portions (2a, 2b) for selectively opening and closing communication between the first and second intake passage portions (2a, 2b); a vacuum tank for storing negative pressure; first and second actuators (43, 44) for independently driving each of the first and second variable intake control valves (11, 12) between an open state and a closed state using the negative pressure in the vacuum tank; and a one-way valve arranged between the vacuum tank and the intake passage for selectively permitting communication between the vacuum tank and the intake passage; the apparatus, being characterised by comprising: control means arranged to control the first and second actuators (43, 44) to offset operating timings of the first and second variable intake control valves (11, 12) when the first and second variable intake control valves (11, 12) are switched according to an increase of the engine rotational speed from a first operating state in which the first and second variable intake control valves (11, 12) are both in the open state by default due to a spring force to a second operating state in which the first and second variable intake control valves (11, 12) are both in the closed state adjusted by the negative pressure. control means arranged to control the first and second actuators (43, 44) to offset operating timings of the first and second variable intake control valves (11, 12) when the first and second variable intake control valves (11, 12) are switched according to an increase of the engine rotational speed from a first operating state in which the first and second variable intake control valves (11, 12) are both in the open state by default due to a spring force to a second operating state in which the first and second variable intake control valves (11, 12) are both in the closed state adjusted by the negative pressure.