Hybrid nanoparticles copper and alumina effect on the heat transfer of thin-film blood flow toward an unsteady permeable stretching sheet is studied. The influence of suction is considered. The governing partial differential equations together with boundary conditions are reduced into the set of ordinary differential equations by implementing the similarity transformations. The Keller-box method is used to solve the momentum and heat equations. The characteristics of the blood flow and heat transfer under the effect of unsteadiness parameter, nanoparticles volume fraction, Casson parameter, and intensity of suction for different thin-film thickness are discussed. The numerical results of the velocity and temperature profiles are graphically displayed. The physical interest such as the local skin friction and Nusselt number are depicted in a tabular form.