The effects of Stefan blowing and the velocity, thermal and solutal slips on bioconvection nanofluid flow over a horizontal moving plate are numerically investigated. The Lie group transformation is introduced to seek similarity solutions of such nano-bioconvection flows for the first time. The reduced governing ordinary differential equations are then numerically solved with Matlab nonlinear equation solver fsolve and ODE solver odel5s. The influences of Stefan blowing, the velocity, thermal and solutal slips, the bioconvection Lewis number, the Lewis number, the velocity, the bioconvection Peclet number and Brownian motion on the dimensionless velocity, temperature, nanoparticle volume fraction, microorganism concentration, the distribution of the density of motile microorganisms, the local skin friction coefficient, the local Nusselt number and the local wall mass flux are analyzed and discussed. The study is relevant to novel microbial fuel cell technologies combining the nanofluid with bioconvection phenomena. (C) 2015 Elsevier Ltd. All rights reserved.