In this study, hybrid nanofluid free convection has been simulated within a permeable domain involving Lorentz effect. To solve and simulate the problem, Control Volume-based Finite Element Method (CVFEM) method is applied. In addition, the non-Darcy model has been used to apply permeable condition in equations. The influence of hybrid nanoparticles (Fe3O4 MWCNT) inside water as base fluid has been studied. Meanwhile, source term of radiation impact has been described for different nanoparticle shapes. The impacts of substantial variables such as Darcy number, radiation factor, magnetic strength and Rayleigh number on nanofluid behavior were fully revealed. It can be concluded that enhancing permeability factor can improve the Nusselt number but reverse behavior can be reported for Lorentz forces.