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Noise pollution is a potential threat to human health and the environment. Using acoustic materials (barriers/insulators and absorbers) in the noise path is a customarily approach for noise control. Nowadays, compared to traditional sound insulating materials (metals, gypsum and concrete), polymers (plastics) have gained more interest among researchers because of their unique features like lightweight, ease of design, low cost, and available state-of-the-art technologies for mass production. Concurrently, the massive amounts of solid waste such as plastic, e-waste, garment waste (textile) and agro residue end up in landfills or are incinerated. Disposal of these solid wastes through landfilling or burning in the air deteriorates the environment. Therefore, in the context of these problems, the present research aims to prepare sound-insulating material by utilizing waste jute fibre (WJF) and recycled plastic (high-density polyethene-rHDPE) through compression moulding. The effect of WJF weight percentage on sound insulation property was studied. The prepared composites were thoroughly characterized for their properties related to sound insulation, i.e., density and tensile strength. The sound transmission loss of the composites was measured as per ASTM-E2611 using a four-microphone impedance tube setup. It was found that with the increase in WJF amount, the sound transmission loss was significantly improved. Moreover, the measured experimental results were compared with the theoretical results computed from mass and stiffness law equations, which showed a good agreement.