The study of the automotive noise reduction has been concentrated on the reduction of the automotive engine noise because the engine noise is the major cause of automotive noise. However, many studies of automotive engine noise led to the interest of the noise reduction of the exhaust and intake system. Recently, the active control method is used to reduce the noise of an automotive exhaust and intake system. It is mostly used the LMS(Least-Mean-Square) algorithm as an algorithm of active control because the LMS algorithm can easily obtain the complex transfer function in real-time. Especially, Filtered-X LMS (FXLMS) algorithm is applied to an Active Noise Control system. However, the convergence performance of LMS algorithm went bad when the FXLMS algorithm was applied to an active control of the induction noise under rapidly accelerated driving conditions. So, in order to solve this problem, the modified FXLMS algorithm is proposed. In this study, the improvement of the control performance using the modified FXLMS algorithm under rapidly and suddenly accelerated driving conditions was identified. Also, the performance of an active control using the LMS algorithm under rapidly accelerated driving conditions was evaluated through the theoretical derivation using a chirp signal to have similar characteristics with the induction noise signal.