Scalar unparticle production in the process is studied from unparticle physics perspective. We have calculated and evaluated the cross sections for muon and Z boson exchange when the beams are initially polarized. Numerical calculations show that the cross section of collisions depends strongly on the polarized condition of the initial beams and the collision energy . The results are plotted in the energy reach available at the present accelerators and the future high energy frontier muon colliders as shown in the scheme by Muon Accelerator Program (MAP) and other different colliders.