The present article numerically investigates the unsteady magnetohydrodynamic (MHD) Couette flow containing novel (Ag + MgO)-water hybrid nanofluid (HNF). The nanoparticles of silver (Ag) and magnesium oxide (MgO) are supplemented to base fluid water. The top wall is kept in uniform motion while the bottom wall of channel set stationary and stretchable. An external magnetic field is applied perpendicular to lower plate. The governed nonlinear partial differential equations (PDE) are solved employing finite difference method (FDM). The effects of hybrid nanofluid and nanofluid (NF) are compared for the significant parameters and presented graphically. The results illustrate that (Ag + MgO)-water HNF exhibits significant influence over Ag-water NF on velocity and temperature in the Couette channel.