Nanofluids have inordinate uses in industries due to their high rate of heat transformation. The enhancement of heat transfer rates, an advanced type of nanofluids called “Hybrid nanofluid” is discovered. Hybrid nanofluids are created by the suspension of two or more type of nano sized atoms in base fluid such as water, oil etc. In current work, the instability of Hydromagnetic Poiseuille flow of thermocapillary layers of liquid of shear thinning hybrid nanofluid of Fe2O3-Fe3O4 in water based fluid is investigated. The transverse magnetic field is imposed on the flow. The solution of obtained ODEs for current problem is found using a numerical method called “cheybeshev collocation method”. The eigenvalue problem from generalized Orr-sommerfeld equations is solved using the algorithm of “QZ” abbreviated as (Qualitat and Zuverlassigkeit). The instability of water based hybrid nanofluids for variation of different parameters are analyzed and discussed through graphs. It has been found that Reynolds number and prandtl number has destabilizing effect on the flow while wave number and magnetic parameter has stabilizing impact on the fluid flow