A boost pressure control apparatus includes a turbocharger whose turbine is rotationally driven by exhaust of an internal combustion engine, and an EGR device, wherein EGR is performed at the time of supercharge, or the EGR amount is increased at the time of supercharge in comparison with when supercharge is not performed. If the internal EGR gas amount is increased by changing opening/closure timings of intake valves and/or exhaust valves via the EGR device, the energy of exhaust can be increased, so that the rotation speed of the turbocharger can be enhanced. Therefore, the responsiveness of boost pressure rise can be enhanced. Thus, a technology of more promptly raising the boost pressure is provided.