This paper concerns with the peristaltic flow of a particle-fluid suspension (as blood model) through asymmetric twodimensional channel with slip conditions. The problem formulation is presented for a duct filled with a compressible viscous fluid mixed with rigid spherical particles. The resulting problems are solved by the perturbation expansion method. The effects of different physical parameters such as particles concentration, compressibility parameter, and slip parameter have a significant effect on velocity distributions and are presented and discussed graphically. It is found that the mean axial velocity increases as the slip parameter increases at a minimal compressibility parameter, and it decreases at a higher value of compressibility parameter with increasing slip parameter. This paper gives a scope for estimating the effects of the slip conditions of two-phase flow characteristics with compressible fluid problems and helps in understanding the role of the engineering applications of pumping solid-fluid mixture by peristaltically driven motion.