The efficient heat transfer performance of hybrid nanofluid making the fluid crucial in many industrial applications like heat exchangers, nuclear reactors, automotive cooling systems, and most manufacturing processes. This study aims to uncover the properties of an unsteady Falkner-Skan hybrid nanofluid flows over a nonlinear moving wedge with the convective boundary condition. The water-based hybrid nanofluid that is considered in this research is composite nanoparticles of copper (Cu) and alumina (Al2O3). The governing partial differential equations are transformed into a set of nonlinear ordinary differential equations by applying suitable similarity variables. Then, the transformed equations are numerically solved by utilizing the Keller-Box method. The effects of various pertinent parameters such as unsteady parameter, moving wedge parameter and the angle wedge parameter on the fluid flows and heat transfer are examined and graphically presented. The moving wedge parameter has enhanced the velocity profile and the heat transfer performance of the fluid. However, an opposite tendency is observed in temperature profiles for the increment of the angle wedge parameter.