The active noise control (ANC) technique has been applied in staggered windows to improve the noise reduction at low frequencies. The control performance of such a system deteriorates significantly at some frequencies where the secondary source cannot radiate effectively due to the reflection at the boundaries of the staggered window. A resonant absorber consisting of a perforated panel and coiled up tubes is proposed to solve the problem. By designing a combination of different absorbers, a proper sound absorption coefficient is achieved around the ineffective frequency. Numerical simulations show that the active sound power reduction increases by 13.5 dB at the frequency with the absorbers attached on one end of the staggered window, and the overall sound power reduction between 100 and 500 Hz increases from 25.9 to 31.2 dB. Attaching the sound absorbers elsewhere in the upstream of the secondary source, for example, on the side walls of the duct also works. The active sound power reduction at 435 Hz increases by 6.3 dB after attaching the absorbers in the experiments, and the noise reduction increment at the evaluation point is 13.6 dB, which agrees with simulation results and demonstrates the feasibility of the proposed sound absorbers.