This study aimed to develop laminate flooring composite using a combination of wood and waste tire rubber (WTR). Plywood panels were produced by using beech (Fagus orientalis), alder (Alnus glutinosa), and poplar (Populus) veneers in a 7-ply configuration. To enhance the physical-mechanical properties of the panels, three loadings of nano-SiO2 (0, 2, and 4 wt%) along with 2 wt% of hexamethyldisilazane (HMDS) were added. Commercial urea-formaldehyde (UF) resin and methylene diphenyl diisocyanate (MDI) were used to bind the wood layers and rubber layers together. The mechanical properties, including modulus of rupture (MOR), modulus of elasticity (MOE), impact strength (IS), hardness strength (HS), and physical properties, such as density (D), water uptake (WU), and thickness swelling (TS), were evaluated. The results showed that increasing the WTR content led to improvements in the physical properties (D, WU, and TS), while negatively affecting the mechanical properties (MOR, MOE, IS, and HS) of the resulting panels. However, the addition of nano-SiO2 improved both the physical and mechanical properties (MOR, MOE, and HS) of the panels. Furthermore, it was observed that the mechanical properties were enhanced with increasing the number of beech layers, although the WU of panels decreased compared to panels made with alder and poplar. Overall, the improvement in the physical properties of the panels followed the order of the arrangement of rubber layers > nano-SiO2 content > veneer layers.