Bioconvection flow of non-Newtonian nanofluids along a horizontal flat plate in a porous medium saturated with gyrotactic microorganisms is investigated by combined group similarity numerical technique. A linear group of transformations is used to develop similarity transformations and the corresponding similarity equations of the governing coupled, nonlinear ordinary differential boundary layer transport equations. The resulting nonlinear boundary value problem with appropriate boundary conditions is solved numerically by an MAPLE software algorithm. The effects of the controlling parameters on the flow, heat, nanoparticle concentration and the density of motile microorganisms characteristic as well as on the local Nusselt, Sherwood and the motile microorganism numbers have been examined. It is found that the bioconvection parameters have strong effects on the flow, heat and mass transfer and motile microorganism numbers. The present study finds application in microbial fuel cells.