Aiming at the noise control of the HVDC converter station, a one-dimensional two-port metamaterial muffler based on the acoustic slow-wave effect is designed and manufactured. The metamaterial muffler achieves a broadband quasi-perfect absorption of noise from 600 to 900 Hz while ensuring a certain ventilation capacity. In addition, the internal equivalent sound velocity curve and the sound pressure and velocity field of the muffler are used to reveal the mechanism of its broadband quasi-perfect sound absorption. The performance of the muffler was verified by theoretical, numerical, and experimental models. The work in this paper is of guiding significance for solving the noise problem in HVDC converter stations.