As an applicable noise attenuator, Helmholtz resonator is mainly used to dampen acoustic noise at low- and medium-frequency ranges. It is typically implemented in combustion-engines and gas turbines to dampen thermoacoustic instabilities. However, it has a narrow effective frequency range and does not work effectively at off-design conditions. In this work, we consider a modified structured Helmholtz resonator (HR) at its neck by applying a rigid baffle in order to maximize its’ noise damping effect and to broaden its frequency bands. The resonator is attached to a cylindrical duct/pipe in presence of a mean flow (grazing flow), aiming to simulate the practical engines flow configuration. For this, a two-dimensional frequency domain numerical model is developed by using COMSOL V5.3. The numerical simulations are carried out by solving the linearized Navier–Stokes equation in frequency domain with low computational cost and time. In order to obtain an optimum design in terms of the maximum noise damping performances, 10 new different configurations/designs are proposed. The effects of 1) the single baffle attached to the upstream or downstream sidewall of the neck ends, that is, Design A, B, C, and D or double baffles, that is, Design E, F, G, and H), 2) the baffle implementation location, 3) the length of the rigid baffle, and 4) the grazing flow low Mach number are evaluated and compared. It is found that Design C is associated with improved TL by 50% and decreased resonant frequency by 20% comparing with the conventional HR. The present preliminary study shows that Design C is the better design. Further experimental and optimization researches are needed to sheds light on the optimum design of a Helmholtz resonator with neck structure being modified, as there is a low Mach number grazing flow.