This present study focuses on the analysis of peristaltic transport involving hybrid nanomaterial fluid through a tapered channel. Peristalsis of hybrid nanomaterial with variable viscosity is studied here. Thermal heat and velocity  with no-slip conditions are considered in the investigation. In order to simplify governing equations small Reynolds number and large wavelength assumptions are used, the exact solution for formulation of stream function , axial velocity and temperature are determined based on the perturbationechnique . In the present study, water is used as a head liquid while nanoparticle contains polystyrene and grapheme oxid. Additionally, main purpose is to explain impacts of  various physical parameter and porosity parameter.  Here, we are concerned with studying the influences of heat transfer  and porous medium on MHD of hybrid nanomaterial which translates through a two, dimensional asymmetric, tapered, channel. Finally, the plot of expressions of velocity curve, temperature distribution and streamlines with trapping phenomena are obtained via Mathematica 11 software.