Sound transmission through narrow ducts is one of the typical but important problem in acoustic field. Recently, acoustic metamaterial has attracted much attention for noise reductions with exotic wave tailoring properties. The unusual phenomenon of acoustic metamaterial is realized by using side-branch resonators, helmholtz resonators or membranes. Especially, side-branch resonators have simple structure and easy to control the target frequencies. This thesis proposes multiple side-branch resonators-based acoustic metamaterials for reduction of noise transmission in a duct. For the objective, the array of side-branch resonator along a duct is treated. By arraying length-varying side branches, it is possible to realize broader bandgap. It is validated by mathematical modeling which contains effective properties of the metamaterial based on effective medium theory. When the length-varying side-branch resonators are arraying they resonate at the difference frequencies therefore the negative bulk modulus are occurred at broad frequency band which lead to broad bandgap. Also transfer matrix is also used which considers the thermo-viscous effect in each side branch. For the efficient reduction performance of the proposed metamaterial, numerous parameter studies are implemented. Based on this parameter studies, selective reduction performance is realized in the given bandgap by controling the gradient of the side branch array. In addition, this study proposes novel side-branch resonators whose resonance frequency can be controlled by adjusting width of side branch. When the upper part of side-branch resonator is wider than the lower part, the resonance frequency is shift to the lower frequency which means the effective length of the side-branch resonator is elongated. On the other hand, when the lower part of side-branch resonator is wider than the upper part, the side-branch resonator resonates at the higher frequency than normal side-branch resonator which means the effective length of the side-branch resonator is shortened. To make clear the mechanism of the reduction performance of novel side-branch resonator, effective medium theory also used to derive the effective properties of the metamaterial and the negative bulk modulus is confirmed. In addition, the transfer matrix validate the result with considering thermo-viscous effect. With various parameter studies, designs of arraying novel side branches are proposed which realize broader bandgap in a compact design domain without any treatment of length. Because of the innovative design and performance of the proposed acoustic metamaterials, the broad application are anticipated in the noise reduction field for the duct.