In this paper, an analysis on a bioconvection flow of a nanofluid past a vertical flat plate in the presence of an out power-law stream is made. The passively controlled nanofluid model is used to approximate this flow problem, which is believed to be physically more realistic than previously commonly used actively controlled nanofluid models. The Lie group transformation method is introduced to seek similarity solutions of such nanobioconvection flows for the first time. The reduced governing equations are then solved numerically with a finite difference technique. Besides, the influences of various parameters such as the Grashof number, the Prandtl number, the bioconvection Rayleigh number, the Lewis number, the bioconvection Péclet number, and the Schimdt number on the distributions of the density of motile micro-organisms profiles, as well as the local skin friction coefficient, the local Nusselt number, the local wall mass flux, and the local density of the motile micro-organisms are analyzed and discussed.