The present investigation reports the synthesis and mechanical properties of a hybrid polymer composite consisting of E-Glass fiber, epoxy and 2 wt.% carbon nanotubes (CNTs) with a varying percentage of natural rubber (NR). The prepared hybrid polymer composites were examined in terms of their surface morphology, thermal properties as well as mechanical properties. The findings from the present study indicate that natural rubber enhances the mechanical properties of the hybrid polymer composites and, in particular, 10 wt.% is the optimum percentage of NR that yields the highest strength of 88 MPa, while the strength is 52 MPa with 5 wt.% NR. In order to evaluate the damping properties, a dynamic mechanical analysis was carried out on the E-Glass/CNT with NR composites at various frequencies along with a thermogravimetric analysis. It was found that the composite reinforced with 10 wt.% natural rubber exhibited a higher glass transition temperature of 376.86 °C and storage modulus of 2468 MPa when compared to the other composites, which indicates the enhanced cross-linking density and higher polymer modulus of the composite. X-ray diffraction analysis was also conducted and the results are reported to improve the general understanding of crystalline phases.